## Ol’shanskiĭ, Grigoriĭ Iosifovich

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 Author ID: olshanskii.grigorii-iosifovich Published as: Olshanski, Grigori; Ol’shanskij, G. I.; Ol’shanskiĭ, G. I.; Olshanski, G. I.; Olshanski, G.; Ol’shanskii, G. I.; Olshanskii, G. I.; Ol’shanskij, G.; Ol’shanskij, Grigorij; Olshanskiĭ, Grigoriĭ; Olshanskiĭ, Grigori; Ol’sanskij, G. I. more...less Homepage: http://www.iitp.ru/en/userpages/88/ External Links: MGP · Math-Net.Ru
 Documents Indexed: 132 Publications since 1969, including 1 Book 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 45 Co-Authors with 60 Joint Publications 1,741 Co-Co-Authors
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### Co-Authors

 72 single-authored 24 Borodin, Alexei 8 Okun’kov, Andreĭ Yur’evich 6 Vershik, Anatoliĭ Moiseevich 5 Gnedin, Alexander V. 4 Kerov, Sergei V. 4 Neretin, Yuriĭ Aleksandrovich 3 Cuenca, Cesar 3 Molev, Alexander I. 3 Nazarov, Maxim Leonidovich 2 Gorin, Vadim 2 Kirillov, Alexandre Aleksandrovich 2 Osinenko, A. A. 2 Regev, Amitai 1 Alekseevskiĭ, Dmitriĭ Vladimirovich 1 Bufetov, Alekseĭ Igor’evich 1 Bugaenko, V. O. 1 Bukhshtaber, Viktor Matveevich 1 Faddeev, Lyudvig Dmitrievich 1 Fomin, Sergey Vladimirovich 1 Gindikin, Simon Grigorevich 1 Gordin, Mikhail Iosifovich 1 Gorin, V. E. 1 Ibragimov, Il’dar Abdullovich 1 Ilyashenko, Yulij Sergeevich 1 Ismagilov, Rais Sal’manovich 1 Kaimanovich, Vadim A. 1 Karabegov, Alexander V. 1 Lando, Sergei K. 1 Lodkin, A. A. 1 Lytvynov, Eugene W. 1 Minlos, Robert Adol’fovich 1 Molchanov, Vladimir Fedorovich 1 Nessonov, Nikolai I. 1 Novikov, Sergeĭ Petrovich 1 Petrov, Fedor Vladimirovich 1 Popov, Vladimir Leonidovich 1 Ryzhikov, Valeriĭ Valentinovich 1 Shkalikov, Andreĭ Andreevich 1 Shvartsman, O. V. 1 Sinaĭ, Yakov Grigor’evich 1 Sosinskiĭ, Alekseĭ Bronislavovich 1 Strahov, Eugene 1 Tikhomirov, Vladimir Mikhaĭlovich 1 Tsfasman, Michael A. 1 Tsilevich, Natalia V.
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### Serials

 20 Functional Analysis and its Applications 7 Russian Mathematical Surveys 6 Communications in Mathematical Physics 6 IMRN. International Mathematics Research Notices 5 Advances in Mathematics 5 Soviet Mathematics. Doklady 5 Journal of Mathematical Sciences (New York) 5 Moscow Mathematical Journal 4 Uspekhi Matematicheskikh Nauk [N. S.] 4 Funktsional’nyĭ Analiz i ego Prilozheniya 4 Comptes Rendus de l’Académie des Sciences. Série I 3 Journal of Functional Analysis 3 Journal of Soviet Mathematics 3 The Electronic Journal of Combinatorics 2 Journal of Algebra 2 Advances in Applied Mathematics 2 Probability Theory and Related Fields 2 Journal of Lie Theory 2 Selecta Mathematica. New Series 2 Mathematical Research Letters 2 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Letters in Mathematical Physics 1 The Annals of Probability 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Matematicheskiĭ Sbornik. Novaya Seriya 1 European Journal of Combinatorics 1 Journal of the American Mathematical Society 1 Leningrad Mathematical Journal 1 The Annals of Applied Probability 1 Differential Geometry and its Applications 1 Mathematics of the USSR, Sbornik 1 St. Petersburg Mathematical Journal 1 Electronic Journal of Probability 1 Séminaire Lotharingien de Combinatoire 1 Transformation Groups 1 Annals of Mathematics. Second Series 1 Cambridge Studies in Advanced Mathematics 1 Translations. Series 2. American Mathematical Society
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### Fields

 56 Topological groups, Lie groups (22-XX) 48 Probability theory and stochastic processes (60-XX) 32 Combinatorics (05-XX) 25 Abstract harmonic analysis (43-XX) 24 Group theory and generalizations (20-XX) 20 Special functions (33-XX) 14 Nonassociative rings and algebras (17-XX) 5 History and biography (01-XX) 5 Quantum theory (81-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Associative rings and algebras (16-XX) 3 Operator theory (47-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Numerical analysis (65-XX)

### Citations contained in zbMATH Open

108 Publications have been cited 1,841 times in 884 Documents Cited by Year
Asymptotics of Plancherel measures for symmetric groups. Zbl 0938.05061
Borodin, Alexei; Okounkov, Andrei; Olshanski, Grigori
2000
Yangians and classical Lie algebras. Zbl 0876.17014
Molev, A.; Nazarov, M.; Ol’shanskij, G.
1996
Shifted Jack polynomials, binomial formula, and applications. Zbl 0995.33013
Okounkov, A.; Olshanski, G.
1997
The boundary of the Young graph with Jack edge multiplicities. Zbl 0960.05107
Kerov, Sergei; Okounkov, Andrei; Olshanski, Grigori
1998
Kerov’s central limit theorem for the Plancherel measure on Young diagrams. Zbl 1016.05073
2002
Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Zbl 1082.43003
Borodin, Alexei; Olshanski, Grigori
2005
The problem of harmonic analysis on the infinite-dimensional unitary group. Zbl 1036.43002
Olshanski, Grigori
2003
Distributions on partitions, point processes, and the hypergeometric kernel. Zbl 0966.60049
Borodin, Alexei; Olshanski, Grigori
2000
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
Asymptotics of Jack polynomials as the number of variables goes to infinity. Zbl 0913.33004
Okounkov, Andrei; Olshanski, Grigori
1998
Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Zbl 0503.22011
Ol’shanskij, G. I.
1982
Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Zbl 0796.43005
Kerov, Serguei; Olshanski, Grigori; Vershik, Anatoli
1993
Polynomial functions on the set of Young diagrams. Zbl 0830.20028
Kerov, Serguei; Olshanski, Grigori
1994
Shifted Schur functions. II: The binomial formula for characters of classical groups and its applications. Zbl 0941.17008
Okounkov, Andrei; Olshanski, Grigori
1998
Point processes and the infinite symmetric group. Zbl 1044.20501
Borodin, Alexei; Olshanski, Grigori
1998
Infinite random matrices and ergodic measures. Zbl 0987.60020
Borodin, Alexei; Olshanski, Grigori
2001
Ergodic unitarily invariant measures on the space of infinite Hermitian matrices. Zbl 0853.22016
Ol’shanskij, Grigorij; Vershik, Anatolij
1996
Markov processes on partitions. Zbl 1105.60052
Borodin, Alexei; Olshanski, Grigori
2006
Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary. Zbl 1260.60149
Borodin, Alexei; Olshanski, Grigori
2012
The boundary of the Gelfand-Tsetlin graph: A new approach. Zbl 1245.05131
Borodin, Alexei; Olshanski, Grigori
2012
Unitary representations of (G,K)-pairs connected with the infinite symmetric group S($$\infty)$$. Zbl 0731.20009
Ol’shanskij, G. I.
1990
Quantized universal enveloping superalgebra of type $$Q$$ and a super- extension of the Hecke algebra. Zbl 0766.17017
Ol’shanskij, G. I.
1992
$$Z$$-measures on partitions and their scaling limits. Zbl 1123.60005
Borodin, Alexei; Olshanski, Grigori
2005
The ASEP and determinantal point processes. Zbl 1369.60031
Borodin, Alexei; Olshanski, Grigori
2017
$$q$$-exchangeability via quasi-invariance. Zbl 1204.60029
Gnedin, Alexander; Olshanski, Grigori
2010
Asymptotics of Plancherel-type random partitions. Zbl 1117.60051
Borodin, Alexei; Olshanski, Grigori
2007
Bethe subalgebras in twisted Yangians. Zbl 0876.17015
Nazarov, Maxim; Olshanski, Grigori
1996
Infinite-dimensional diffusions as limits of random walks on partitions. Zbl 1163.60036
Borodin, Alexei; Olshanski, Grigori
2009
Random partitions and the gamma kernel. Zbl 1128.60301
Borodin, Alexei; Olshanski, Grigori
2005
Harmonic functions on multiplicative graphs and interpolation polynomials. Zbl 0939.05082
Borodin, Alexei; Olshanski, Grigori
2000
An introduction to harmonic analysis on the infinite symmetric group. Zbl 1035.05100
Olshanski, Grigori
2003
Stochastic dynamics related to Plancherel measure on partitions. Zbl 1109.60041
Borodin, Alexei; Olshanski, Grigori
2006
Limits of $$BC$$-type orthogonal polynomials as the number of variables goes to infinity. Zbl 1151.33008
Okounkov, Andrei; Olshanski, Grigori
2006
$$z$$-measures on partitions, Robinson-Schensted-Knuth correspondence, and $$\beta=2$$ random matrix ensembles. Zbl 0987.15013
Borodin, Alexei; Olshanski, Grigori
2001
The Young bouquet and its boundary. Zbl 1320.05137
Borodin, Alexei; Olshanski, Grigori
2013
Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams. Zbl 1102.05001
Gnedin, Alexander; Olshanski, Grigori
2006
Convex cones in symmetric Lie algebras, Lie semigroups and invariant causal (order) structures on pseudo-Riemannian symmetric spaces. Zbl 0512.22012
Ol’shanskij, G. I.
1982
Representations of the infinite symmetric group. Zbl 1364.20001
Borodin, Alexei; Olshanski, Grigori
2016
The two-sided infinite extension of the Mallows model for random permutations. Zbl 1242.60010
Gnedin, Alexander; Olshanski, Grigori
2012
The quasi-invariance property for the gamma kernel determinantal measure. Zbl 1218.60004
Olshanski, Grigori
2011
A quantization of the harmonic analysis on the infinite-dimensional unitary group. Zbl 1328.43007
2016
Meixner polynomials and random partitions. Zbl 1126.60006
Borodin, Alexei; Olshanski, Grigori
2006
On semigroups related to infinite-dimensional groups. Zbl 0736.22014
Ol’shanskij, G. I.
1991
Classification of irreducible representations of groups of automorphisms of Bruhat-Tits trees. Zbl 0371.22014
Ol’shanskii, G. I.
1977
Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. Zbl 0739.22015
Ol’shanskij, G. I.
1991
Representation theory and random point processes. Zbl 1087.15025
Borodin, Alexei; Olshanski, Grigori
2005
Limit shapes for growing extreme characters of $$U(\infty)$$. Zbl 1325.60013
Borodin, Alexei; Bufetov, Alexey; Olshanski, Grigori
2015
Giambelli compatible point processes. Zbl 1108.05093
Borodin, Alexei; Olshanski, Grigori; Strahov, Eugene
2006
Extension of the algebra $${\mathcal U}({\mathfrak g})$$ for infinite-dimensional classical Lie algebras $${\mathfrak g}$$ and the Yangians $$Y(\mathfrak{gl}(m))$$. Zbl 0662.22016
Ol’shanskij, G. I.
1988
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
Laguerre and Meixner orthogonal bases in the algebra of symmetric functions. Zbl 1257.33015
Olshanski, Grigori
2012
Plancherel averages: remarks on a paper by Stanley. Zbl 1193.05161
Olshanski, Grigori
2010
Multivariate Jacobi polynomials and the Selberg integral. Zbl 1306.43006
Olshanski, G. I.; Osinenko, A. A.
2012
Markov dynamics on the Thoma cone: a model of time-dependent determinantal processes with infinitely many particles. Zbl 1293.60074
Borodin, Alexei; Olshanski, Grigori
2013
Centralizer construction for twisted Yangians. Zbl 1026.17021
Molev, Alexander; Olshanski, Grigori
2000
New ”large” groups of type I. Zbl 0484.22027
Ol’shanskij, G. I.
1982
Twisted Yangians and infinite-dimensional classical Lie algebras. Zbl 0780.17025
Ol’shanskiĭ, G. I.
1992
Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines. Zbl 1281.22003
Olshanski, Grigori
2013
Invariant orderings in simple Lie groups: Solution of a problem of Eh. B. Vinberg. Zbl 0576.32040
Ol’shanskij, G. I.
1983
Infinite-dimensional classical groups of finite $$r$$-rank: description of representations and asymptotic theory. Zbl 0545.22020
Ol’shanskiĭ, G. I.
1984
Unitary representations of infinite dimensional pairs (G,K) and the formalism of R. Howe. Zbl 0724.22020
Ol’shanskij, G. I.
1990
Unitary representations of the infinite-dimensional classical groups $$\text{U}(p,\,\infty)$$, $$\text{SO}_0(p,\,\infty)$$, $$\text{Sp}(p,\,\infty)$$, and of the corresponding motion groups. Zbl 0392.22012
Ol’shanskiĭ, G. I.
1978
A $$q$$-analogue of de Finetti’s theorem. Zbl 1200.60029
Gnedin, Alexander; Olshanski, Grigori
2009
Anisotropic Young diagrams and infinite-dimensional diffusion processes with the Jack parameter. Zbl 1193.60097
Olshanski, Grigori
2010
Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes. Zbl 1296.33021
Olshanski, G.
2011
Unitary representations of infinite-dimensional pairs $$(G,K)$$ and the formalism of R. Howe. Zbl 0532.22019
Ol’shanskiĭ, G. I.
1983
Complex Lie semigroups, Hardy spaces and the Gel’fand-Gindikin program. Zbl 0789.22011
Ol’shanskij, G. I.
1991
Point processes related to the infinite symmetric group. Zbl 1087.60041
Olshanski, Grigori
2003
The boundary of Eulerian number triangle. Zbl 1126.60065
Gnedin, Alexander; Olshanski, Grigori
2006
Difference operators and determinantal point processes. Zbl 1157.60319
Olshanski, Grigori
2008
Random permutations and related topics. Zbl 1242.05006
Olshanski, Grigori
2011
Boundary values of holomorphic functions, singular unitary representations of $$O(p,q)$$, and their limits as $$q\to\infty$$. Zbl 0909.22025
Neretin, Yu. A.; Ol’shanskii, G. I.
1995
Classification of the irreducible representations of the automorphism groups of Bruhat-Tits trees. Zbl 0359.22010
Ol’shanskiĭ, G. I.
1977
Semigroups generated by the Weil representation of the infinite-dimensional symplectic group. (Semi-groupes engendrés par la représentation de Weil du groupe symplectique de dimension infinie.) Zbl 0709.43007
Nazarov, Maxime; Neretin, Yuriĭ; Olshanskiĭ, Grigoriĭ
1989
Intertwining operators and complementary series in the class of representations of the full matrix group over a locally compact division algebra that are induced by parabolic subgroups. Zbl 0298.22016
Ol’shanskiĭ, G. I.
1974
Method of holomorphic extensions in the theory of unitary representations of infinite-dimensional classical groups. Zbl 0668.22008
Ol’shanskij, G. I.
1988
Description of unitary representations with highest weight for groups U(p,q). Zbl 0455.22004
Ol’shanskij, G. I.
1981
Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities. Zbl 1075.43009
Ol’shanskij, G. I.
2003
An analogue of the big $$q$$-Jacobi polynomials in the algebra of symmetric functions. Zbl 1381.33021
Olshanski, G. I.
2017
Unitary representations of the infinite-dimensional classical groups U(p,infinity), SO//0(p,infinity), Sp(p,infinity) and the corresponding motion groups. Zbl 0411.22017
Ol’shanskij, G. I.
1979
Random Young tableaux and combinatorial identities. Zbl 0982.05110
Olshanski, Grigori; Regev, Amitai
2001
Extended Gelfand-Tsetlin graph, its $$q$$-boundary, and $$q$$-B-splines. Zbl 1358.43009
Olshanski, G. I.
2016
Unitary representations of the group $$SO_ 0(\infty,\infty)$$ as limits of unitary representations of the groups $$SO_ 0(n,\infty)$$ as n$$\to \infty$$. Zbl 0628.22009
Ol’shanskij, G. I.
1986
Interpolation Macdonald polynomials and Cauchy-type identities. Zbl 1401.05301
Olshanski, Grigori
2019
Markov dynamics on the dual object to the infinite-dimensional unitary group. Zbl 1388.60134
Olshanski, Grigori
2016
Weil representation and norms of Gaussian operators. Zbl 0848.22017
Ol’shanskij, G. I.
1994
Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Zbl 0990.20005
Molev, A. I.; Olshanski, G. I.
2001
The representation ring of the unitary groups and Markov processes of algebraic origin. Zbl 1359.22016
Olshanski, Grigori
2016
Yangians and universal enveloping algebras. Zbl 0691.17005
Ol’shanskij, G. I.
1989
On the duality theorem of Frobenius. Zbl 0234.22012
Ol’shanskij, G. I.
1969
Description of unitary representations with highest weight for the groups U(p,q). Zbl 0439.22019
Ol’shanskij, G. I.
1980
Intertwining operators and complementary series in the class of representations of the full matrix group over a locally compact division algebra that are induced by parabolic subgroups. Zbl 0309.22014
Ol’shanskiĭ, G. I.
1975
The Gelfand-Tsetlin graph and Markov processes. Zbl 1373.05203
Olshanski, Grigori
2014
Multivariate Jacobi polynomials and the Selberg integral. II. Zbl 1347.43004
Olshanski, G.; Osinenko, A.
2016
Approximation of Markov dynamics on the dual object of the infinite-dimensional unitary group. Zbl 1343.60112
Olshanski, G. I.
2015
Determinantal measures related to big $$q$$-Jacobi polynomials. Zbl 1376.60016
Gorin, V. E.; Olshanski, G. I.
2015
Generalized characters of $$U(\infty)$$ and inner functions. (Caractères généralisés de $$U(\infty)$$ et fonctions intérieures.) Zbl 0790.43009
Olshanskiĭ, Grigori
1991
Yangians and universal enveloping algebras. Zbl 0668.17009
Ol’shanskij, G. I.
1987
Unitary representations of the infinite symmetric group: a semigroup approach. Zbl 0605.22005
Ol’shanskij, G. I.
1985
Spherical functions and characters on the group U(infinity)*. Zbl 0497.22023
Ol’shanskij, G. I.
1982
Determinantal point processes and fermion quasifree states. Zbl 1464.60045
Olshanski, Grigori
2020
Interpolation Macdonald polynomials and Cauchy-type identities. Zbl 1401.05301
Olshanski, Grigori
2019
The topological support of the z-measures on the Thoma simplex. Zbl 1422.43001
Olshanski, G. I.
2018
The ASEP and determinantal point processes. Zbl 1369.60031
Borodin, Alexei; Olshanski, Grigori
2017
An analogue of the big $$q$$-Jacobi polynomials in the algebra of symmetric functions. Zbl 1381.33021
Olshanski, G. I.
2017
Representations of the infinite symmetric group. Zbl 1364.20001
Borodin, Alexei; Olshanski, Grigori
2016
A quantization of the harmonic analysis on the infinite-dimensional unitary group. Zbl 1328.43007
2016
Extended Gelfand-Tsetlin graph, its $$q$$-boundary, and $$q$$-B-splines. Zbl 1358.43009
Olshanski, G. I.
2016
Markov dynamics on the dual object to the infinite-dimensional unitary group. Zbl 1388.60134
Olshanski, Grigori
2016
The representation ring of the unitary groups and Markov processes of algebraic origin. Zbl 1359.22016
Olshanski, Grigori
2016
Multivariate Jacobi polynomials and the Selberg integral. II. Zbl 1347.43004
Olshanski, G.; Osinenko, A.
2016
Diffusion processes on the Thoma cone. Zbl 1357.60085
Olshanski, G. I.
2016
Limit shapes for growing extreme characters of $$U(\infty)$$. Zbl 1325.60013
Borodin, Alexei; Bufetov, Alexey; Olshanski, Grigori
2015
Approximation of Markov dynamics on the dual object of the infinite-dimensional unitary group. Zbl 1343.60112
Olshanski, G. I.
2015
Determinantal measures related to big $$q$$-Jacobi polynomials. Zbl 1376.60016
Gorin, V. E.; Olshanski, G. I.
2015
The Gelfand-Tsetlin graph and Markov processes. Zbl 1373.05203
Olshanski, Grigori
2014
The Young bouquet and its boundary. Zbl 1320.05137
Borodin, Alexei; Olshanski, Grigori
2013
Markov dynamics on the Thoma cone: a model of time-dependent determinantal processes with infinitely many particles. Zbl 1293.60074
Borodin, Alexei; Olshanski, Grigori
2013
Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines. Zbl 1281.22003
Olshanski, Grigori
2013
Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary. Zbl 1260.60149
Borodin, Alexei; Olshanski, Grigori
2012
The boundary of the Gelfand-Tsetlin graph: A new approach. Zbl 1245.05131
Borodin, Alexei; Olshanski, Grigori
2012
The two-sided infinite extension of the Mallows model for random permutations. Zbl 1242.60010
Gnedin, Alexander; Olshanski, Grigori
2012
Laguerre and Meixner orthogonal bases in the algebra of symmetric functions. Zbl 1257.33015
Olshanski, Grigori
2012
Multivariate Jacobi polynomials and the Selberg integral. Zbl 1306.43006
Olshanski, G. I.; Osinenko, A. A.
2012
The quasi-invariance property for the gamma kernel determinantal measure. Zbl 1218.60004
Olshanski, Grigori
2011
Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes. Zbl 1296.33021
Olshanski, G.
2011
Random permutations and related topics. Zbl 1242.05006
Olshanski, Grigori
2011
$$q$$-exchangeability via quasi-invariance. Zbl 1204.60029
Gnedin, Alexander; Olshanski, Grigori
2010
Plancherel averages: remarks on a paper by Stanley. Zbl 1193.05161
Olshanski, Grigori
2010
Anisotropic Young diagrams and infinite-dimensional diffusion processes with the Jack parameter. Zbl 1193.60097
Olshanski, Grigori
2010
Infinite-dimensional diffusions as limits of random walks on partitions. Zbl 1163.60036
Borodin, Alexei; Olshanski, Grigori
2009
A $$q$$-analogue of de Finetti’s theorem. Zbl 1200.60029
Gnedin, Alexander; Olshanski, Grigori
2009
Difference operators and determinantal point processes. Zbl 1157.60319
Olshanski, Grigori
2008
Asymptotics of Plancherel-type random partitions. Zbl 1117.60051
Borodin, Alexei; Olshanski, Grigori
2007
Markov processes on partitions. Zbl 1105.60052
Borodin, Alexei; Olshanski, Grigori
2006
Stochastic dynamics related to Plancherel measure on partitions. Zbl 1109.60041
Borodin, Alexei; Olshanski, Grigori
2006
Limits of $$BC$$-type orthogonal polynomials as the number of variables goes to infinity. Zbl 1151.33008
Okounkov, Andrei; Olshanski, Grigori
2006
Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams. Zbl 1102.05001
Gnedin, Alexander; Olshanski, Grigori
2006
Meixner polynomials and random partitions. Zbl 1126.60006
Borodin, Alexei; Olshanski, Grigori
2006
Giambelli compatible point processes. Zbl 1108.05093
Borodin, Alexei; Olshanski, Grigori; Strahov, Eugene
2006
The boundary of Eulerian number triangle. Zbl 1126.60065
Gnedin, Alexander; Olshanski, Grigori
2006
Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Zbl 1082.43003
Borodin, Alexei; Olshanski, Grigori
2005
$$Z$$-measures on partitions and their scaling limits. Zbl 1123.60005
Borodin, Alexei; Olshanski, Grigori
2005
Random partitions and the gamma kernel. Zbl 1128.60301
Borodin, Alexei; Olshanski, Grigori
2005
Representation theory and random point processes. Zbl 1087.15025
Borodin, Alexei; Olshanski, Grigori
2005
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
The problem of harmonic analysis on the infinite-dimensional unitary group. Zbl 1036.43002
Olshanski, Grigori
2003
An introduction to harmonic analysis on the infinite symmetric group. Zbl 1035.05100
Olshanski, Grigori
2003
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
Point processes related to the infinite symmetric group. Zbl 1087.60041
Olshanski, Grigori
2003
Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities. Zbl 1075.43009
Ol&rsquo;shanskij, G. I.
2003
Kerov’s central limit theorem for the Plancherel measure on Young diagrams. Zbl 1016.05073
2002
Infinite random matrices and ergodic measures. Zbl 0987.60020
Borodin, Alexei; Olshanski, Grigori
2001
$$z$$-measures on partitions, Robinson-Schensted-Knuth correspondence, and $$\beta=2$$ random matrix ensembles. Zbl 0987.15013
Borodin, Alexei; Olshanski, Grigori
2001
Random Young tableaux and combinatorial identities. Zbl 0982.05110
Olshanski, Grigori; Regev, Amitai
2001
Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Zbl 0990.20005
Molev, A. I.; Olshanski, G. I.
2001
Asymptotics of Plancherel measures for symmetric groups. Zbl 0938.05061
Borodin, Alexei; Okounkov, Andrei; Olshanski, Grigori
2000
Distributions on partitions, point processes, and the hypergeometric kernel. Zbl 0966.60049
Borodin, Alexei; Olshanski, Grigori
2000
Harmonic functions on multiplicative graphs and interpolation polynomials. Zbl 0939.05082
Borodin, Alexei; Olshanski, Grigori
2000
Centralizer construction for twisted Yangians. Zbl 1026.17021
Molev, Alexander; Olshanski, Grigori
2000
The boundary of the Young graph with Jack edge multiplicities. Zbl 0960.05107
Kerov, Sergei; Okounkov, Andrei; Olshanski, Grigori
1998
Asymptotics of Jack polynomials as the number of variables goes to infinity. Zbl 0913.33004
Okounkov, Andrei; Olshanski, Grigori
1998
Shifted Schur functions. II: The binomial formula for characters of classical groups and its applications. Zbl 0941.17008
Okounkov, Andrei; Olshanski, Grigori
1998
Point processes and the infinite symmetric group. Zbl 1044.20501
Borodin, Alexei; Olshanski, Grigori
1998
Shifted Jack polynomials, binomial formula, and applications. Zbl 0995.33013
Okounkov, A.; Olshanski, G.
1997
Generalized symmetrization in enveloping algebras. Zbl 0964.17007
Olshanski, Grigori
1997
Yangians and classical Lie algebras. Zbl 0876.17014
Molev, A.; Nazarov, M.; Ol&rsquo;shanskij, G.
1996
Ergodic unitarily invariant measures on the space of infinite Hermitian matrices. Zbl 0853.22016
Ol&rsquo;shanskij, Grigorij; Vershik, Anatolij
1996
Bethe subalgebras in twisted Yangians. Zbl 0876.17015
Nazarov, Maxim; Olshanski, Grigori
1996
Boundary values of holomorphic functions, singular unitary representations of $$O(p,q)$$, and their limits as $$q\to\infty$$. Zbl 0909.22025
Neretin, Yu. A.; Ol&rsquo;shanskii, G. I.
1995
Cauchy-Szegö kernels for Hardy spaces on simple Lie groups. Zbl 0860.43008
Olshanski, Grigori
1995
Polynomial functions on the set of Young diagrams. Zbl 0830.20028
Kerov, Serguei; Olshanski, Grigori
1994
Weil representation and norms of Gaussian operators. Zbl 0848.22017
Ol&rsquo;shanskij, G. I.
1994
Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Zbl 0796.43005
Kerov, Serguei; Olshanski, Grigori; Vershik, Anatoli
1993
Quantized universal enveloping superalgebra of type $$Q$$ and a super- extension of the Hecke algebra. Zbl 0766.17017
Ol&rsquo;shanskij, G. I.
1992
Twisted Yangians and infinite-dimensional classical Lie algebras. Zbl 0780.17025
Ol&rsquo;shanskiĭ, G. I.
1992
On semigroups related to infinite-dimensional groups. Zbl 0736.22014
Ol&rsquo;shanskij, G. I.
1991
Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. Zbl 0739.22015
Ol&rsquo;shanskij, G. I.
1991
Complex Lie semigroups, Hardy spaces and the Gel’fand-Gindikin program. Zbl 0789.22011
Ol&rsquo;shanskij, G. I.
1991
Generalized characters of $$U(\infty)$$ and inner functions. (Caractères généralisés de $$U(\infty)$$ et fonctions intérieures.) Zbl 0790.43009
Olshanskiĭ, Grigori
1991
Unitary representations of (G,K)-pairs connected with the infinite symmetric group S($$\infty)$$. Zbl 0731.20009
Ol&rsquo;shanskij, G. I.
1990
Unitary representations of infinite dimensional pairs (G,K) and the formalism of R. Howe. Zbl 0724.22020
Ol&rsquo;shanskij, G. I.
1990
Semigroups generated by the Weil representation of the infinite-dimensional symplectic group. (Semi-groupes engendrés par la représentation de Weil du groupe symplectique de dimension infinie.) Zbl 0709.43007
Nazarov, Maxime; Neretin, Yuriĭ; Olshanskiĭ, Grigoriĭ
1989
Yangians and universal enveloping algebras. Zbl 0691.17005
Ol&rsquo;shanskij, G. I.
1989
Extension of the algebra $${\mathcal U}({\mathfrak g})$$ for infinite-dimensional classical Lie algebras $${\mathfrak g}$$ and the Yangians $$Y(\mathfrak{gl}(m))$$. Zbl 0662.22016
Ol&rsquo;shanskij, G. I.
1988
Method of holomorphic extensions in the theory of unitary representations of infinite-dimensional classical groups. Zbl 0668.22008
Ol&rsquo;shanskij, G. I.
1988
Yangians and universal enveloping algebras. Zbl 0668.17009
Ol&rsquo;shanskij, G. I.
1987
Unitary representations of the group $$SO_ 0(\infty,\infty)$$ as limits of unitary representations of the groups $$SO_ 0(n,\infty)$$ as n$$\to \infty$$. Zbl 0628.22009
Ol&rsquo;shanskij, G. I.
1986
Unitary representations of the infinite symmetric group: a semigroup approach. Zbl 0605.22005
Ol&rsquo;shanskij, G. I.
1985
Infinite-dimensional classical groups of finite $$r$$-rank: description of representations and asymptotic theory. Zbl 0545.22020
Ol&rsquo;shanskiĭ, G. I.
1984
Invariant orderings in simple Lie groups: Solution of a problem of Eh. B. Vinberg. Zbl 0576.32040
Ol&rsquo;shanskij, G. I.
1983
Unitary representations of infinite-dimensional pairs $$(G,K)$$ and the formalism of R. Howe. Zbl 0532.22019
Ol&rsquo;shanskiĭ, G. I.
1983
Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Zbl 0503.22011
Ol&rsquo;shanskij, G. I.
1982
Convex cones in symmetric Lie algebras, Lie semigroups and invariant causal (order) structures on pseudo-Riemannian symmetric spaces. Zbl 0512.22012
Ol&rsquo;shanskij, G. I.
1982
New ”large” groups of type I. Zbl 0484.22027
Ol&rsquo;shanskij, G. I.
1982
Spherical functions and characters on the group U(infinity)*. Zbl 0497.22023
Ol&rsquo;shanskij, G. I.
1982
Spherical functions and characters on the group $$U(\infty)^X$$. Zbl 0506.22021
Ol&rsquo;shanskij, G. I.
1982
Description of unitary representations with highest weight for groups U(p,q). Zbl 0455.22004
Ol&rsquo;shanskij, G. I.
1981
Description of unitary representations with highest weight for the groups U(p,q). Zbl 0439.22019
Ol&rsquo;shanskij, G. I.
1980
Unitary representations of the infinite-dimensional classical groups U(p,infinity), SO//0(p,infinity), Sp(p,infinity) and the corresponding motion groups. Zbl 0411.22017
Ol&rsquo;shanskij, G. I.
1979
...and 8 more Documents
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### Cited by 738 Authors

 55 Borodin, Alexei 45 Ol’shanskiĭ, Grigoriĭ Iosifovich 27 Neretin, Yuriĭ Aleksandrovich 25 Gorin, Vadim 19 Molev, Alexander I. 19 Vershik, Anatoliĭ Moiseevich 17 Bufetov, Aleksandr Igorevich 17 Hilgert, Joachim 17 Neeb, Karl-Hermann 16 Petrov, Leonid 15 Ragoucy, Eric 14 Assiotis, Theodoros 14 Corwin, Ivan Z. 13 Bufetov, Alekseĭ Igor’evich 11 Okun’kov, Andreĭ Yur’evich 11 Śniady, Piotr 10 Crampé, Nicolas 10 Qiu, Yanqi 9 Doikou, Anastasia 9 Féray, Valentin 9 Fulman, Jason E. 9 Hofmann, Karl Heinrich 8 Cuenca, Cesar 8 Guay, Nicolas 8 Kerov, Sergei V. 8 Lassalle, Michel 8 Strahov, Eugene 7 Ferrari, Patrik Lino 7 Frappat, Luc 7 Najnudel, Joseph 6 Betea, Dan 6 Kang, Seok-Jin 6 Lopushanski, Oleh V. 6 Matsumoto, Sho 6 Nazarov, Maxim Leonidovich 6 Nikeghbali, Ashkan 6 Rains, Eric M. 6 Sergeev, Aleksandr Nikolaevich 5 Arnaudon, Daniel 5 Blower, Gordon 5 Gnedin, Alexander V. 5 Gorin, V. E. 5 Grantcharov, Dimitar 5 Jing, Naihuan 5 Jung, Ji Hye 5 Mukhin, Evgeny 5 Orlov, Aleksandr Yu. 5 Ørsted, Bent 5 Regelskis, Vidas 5 Rybnikov, Leonid Grigor’evich 5 Varchenko, Alexander Nikolaevich 5 Veselov, Alexander Petrovich 5 Warnaar, S. Ole 4 Adler, Mark 4 Brundan, Jonathan 4 Chicherin, Dmitry 4 Derkachëv, Sergeĭ Èduardovich 4 Diaconis, Persi Warren 4 Duits, Maurice 4 Feĭgin, Boris L’vovich 4 Forrester, Peter J. 4 Ghosal, Promit 4 Han, Guo-Niu 4 Khoroshkin, Sergey M. 4 Kim, Myungho 4 Kuan, Jeffrey 4 Kuhn, Maria Gabriella 4 Martínez-Finkelshtein, Andrei 4 Mironov, Andrei D. 4 Ólafsson, Gestur 4 Osinenko, A. A. 4 Panova, Greta 4 Romik, Dan 4 Shadrin, Sergey V. 4 Tarasov, Vitaly Olegovich 4 Tsilevich, Natalia V. 4 van Moerbeke, Pierre 4 Webb, Christian 3 Albeverio, Sergio A. 3 Avan, Jean 3 Barraquand, Guillaume 3 Beltiţă, Daniel 3 Benkart, Georgia M. 3 Bouali, Mohamed 3 Bouttier, Jérémie 3 Charlier, Christophe 3 Deift, Percy A. 3 Diaz, Pablo 3 Dimitrov, Evgeni I. 3 Dołȩga, Maciej 3 Dörr, Norbert 3 Frassek, Rouven 3 Harnad, John 3 Hivert, Florent 3 Holroyd, Alexander E. 3 Hora, Akihito 3 Itoh, Minoru 3 Jiang, Tiefeng 3 Johansson, Kurt 3 Kammoun, Mohamed Slim ...and 638 more Authors
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### Cited in 170 Serials

 54 Advances in Mathematics 41 Communications in Mathematical Physics 39 Journal of Mathematical Sciences (New York) 35 Functional Analysis and its Applications 27 Journal of Mathematical Physics 27 Journal of Functional Analysis 24 The Annals of Probability 24 Journal of Algebra 22 Transactions of the American Mathematical Society 21 Letters in Mathematical Physics 19 Probability Theory and Related Fields 19 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 17 Advances in Applied Mathematics 16 Journal of Statistical Physics 15 Selecta Mathematica. New Series 13 Annales de l’Institut Fourier 13 Duke Mathematical Journal 13 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 12 Mathematische Annalen 12 Journal of Algebraic Combinatorics 11 Nuclear Physics. B 11 Journal of High Energy Physics 11 Journal of Statistical Mechanics: Theory and Experiment 9 Journal of Theoretical Probability 9 Electronic Journal of Probability 8 Compositio Mathematica 8 Inventiones Mathematicae 8 Proceedings of the American Mathematical Society 8 Stochastic Processes and their Applications 8 Bulletin of the American Mathematical Society. New Series 7 Discrete Mathematics 7 Theoretical and Mathematical Physics 7 Journal of Approximation Theory 7 Journal of Combinatorial Theory. Series A 7 Mathematische Zeitschrift 7 Annales Henri Poincaré 6 Journal of Geometry and Physics 6 The Electronic Journal of Combinatorics 6 Bernoulli 6 Séminaire Lotharingien de Combinatoire 6 Transformation Groups 6 Representation Theory 5 Communications on Pure and Applied Mathematics 5 Rocky Mountain Journal of Mathematics 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Semigroup Forum 5 European Journal of Combinatorics 5 Journal of the American Mathematical Society 5 The Ramanujan Journal 5 Random Matrices: Theory and Applications 4 Journal of Mathematical Analysis and Applications 4 Arkiv för Matematik 4 Monatshefte für Mathematik 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 The Annals of Applied Probability 4 Annals of Combinatorics 4 Proceedings of the Steklov Institute of Mathematics 3 Russian Mathematical Surveys 3 Journal of Applied Probability 3 Manuscripta Mathematica 3 Nagoya Mathematical Journal 3 Results in Mathematics 3 Indagationes Mathematicae. New Series 3 Izvestiya: Mathematics 3 Algebras and Representation Theory 3 Journal of Physics A: Mathematical and Theoretical 2 International Journal of Modern Physics A 2 Communications in Algebra 2 Israel Journal of Mathematics 2 Mathematical Notes 2 Nonlinearity 2 Physics Letters. B 2 Reviews in Mathematical Physics 2 American Journal of Mathematics 2 Publications Mathématiques 2 Integral Equations and Operator Theory 2 Journal of the Mathematical Society of Japan 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Transactions of the Moscow Mathematical Society 2 Physica D 2 Constructive Approximation 2 International Journal of Mathematics 2 Random Structures & Algorithms 2 Differential Geometry and its Applications 2 Geometric and Functional Analysis. GAFA 2 Combinatorics, Probability and Computing 2 Electronic Communications in Probability 2 Sbornik: Mathematics 2 Abstract and Applied Analysis 2 Mathematical Physics, Analysis and Geometry 2 Geometry & Topology 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Annals of Mathematics. Second Series 2 Journal of the European Mathematical Society (JEMS) 2 Czechoslovak Journal of Physics 2 Journal of the Australian Mathematical Society 2 Moscow Mathematical Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Groups, Geometry, and Dynamics 2 Japanese Journal of Mathematics. 3rd Series ...and 70 more Serials
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### Cited in 52 Fields

 333 Probability theory and stochastic processes (60-XX) 245 Combinatorics (05-XX) 153 Topological groups, Lie groups (22-XX) 145 Nonassociative rings and algebras (17-XX) 142 Group theory and generalizations (20-XX) 121 Statistical mechanics, structure of matter (82-XX) 105 Quantum theory (81-XX) 96 Special functions (33-XX) 85 Abstract harmonic analysis (43-XX) 82 Linear and multilinear algebra; matrix theory (15-XX) 44 Associative rings and algebras (16-XX) 42 Dynamical systems and ergodic theory (37-XX) 41 Functional analysis (46-XX) 40 Operator theory (47-XX) 35 Algebraic geometry (14-XX) 26 Differential geometry (53-XX) 25 Number theory (11-XX) 23 Partial differential equations (35-XX) 23 Harmonic analysis on Euclidean spaces (42-XX) 21 Statistics (62-XX) 19 Measure and integration (28-XX) 16 Ordinary differential equations (34-XX) 14 Functions of a complex variable (30-XX) 14 Several complex variables and analytic spaces (32-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 9 Convex and discrete geometry (52-XX) 9 Manifolds and cell complexes (57-XX) 7 Difference and functional equations (39-XX) 7 Approximations and expansions (41-XX) 7 Relativity and gravitational theory (83-XX) 6 Numerical analysis (65-XX) 6 Biology and other natural sciences (92-XX) 4 Category theory; homological algebra (18-XX) 4 Potential theory (31-XX) 4 Integral transforms, operational calculus (44-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 General topology (54-XX) 3 Computer science (68-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Mathematical logic and foundations (03-XX) 2 Integral equations (45-XX) 2 Algebraic topology (55-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 $$K$$-theory (19-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX)