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## Ol’shanskiĭ, Grigoriĭ Iosifovich

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 Author ID: olshanskii.grigorii-iosifovich Published as: Ol’sanskij, G. I.; Ol’shanskii, G. I.; Ol’shanskij, G.; Ol’shanskij, G. I.; Ol’shanskij, Grigorij; Ol’shanskiĭ, G. I.; Olshanski, G.; Olshanski, G. I.; Olshanski, Grigori; Olshanskii, G. I.; Olshanskiĭ, Grigori; Olshanskiĭ, Grigoriĭ Homepage: http://www.iitp.ru/en/userpages/88/ External Links: MGP · Math-Net.Ru
 Documents Indexed: 128 Publications since 1969, including 2 Books Biographic References: 1 Publication
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all top 5

#### Serials

 20 Functional Analysis and its Applications 7 Russian Mathematical Surveys 5 Communications in Mathematical Physics 5 Soviet Mathematics. Doklady 5 IMRN. International Mathematics Research Notices 5 Journal of Mathematical Sciences (New York) 4 Uspekhi Matematicheskikh Nauk [N. S.] 4 Advances in Mathematics 4 Funktsional’nyĭ Analiz i ego Prilozheniya 4 Comptes Rendus de l’Académie des Sciences. Série I 4 Moscow Mathematical Journal 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 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 Selecta Mathematica. New Series 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
all top 5

#### Fields

 55 Topological groups, Lie groups (22-XX) 45 Probability theory and stochastic processes (60-XX) 29 Combinatorics (05-XX) 25 Abstract harmonic analysis (43-XX) 23 Group theory and generalizations (20-XX) 17 Special functions (33-XX) 14 Nonassociative rings and algebras (17-XX) 5 History and biography (01-XX) 5 Quantum theory (81-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Associative rings and algebras (16-XX) 3 Operator theory (47-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Functional analysis (46-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Potential theory (31-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 1,736 times in 823 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
Ivanov, Vladimir; Olshanski, Grigori
2002
Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Zbl 1082.43003
Borodin, Alexei; Olshanski, Grigori
2005
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
Distributions on partitions, point processes, and the hypergeometric kernel. Zbl 0966.60049
Borodin, Alexei; Olshanski, Grigori
2000
The problem of harmonic analysis on the infinite-dimensional unitary group. Zbl 1036.43002
Olshanski, Grigori
2003
Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Zbl 0503.22011
Ol’shanskij, G. I.
1982
Asymptotics of Jack polynomials as the number of variables goes to infinity. Zbl 0913.33004
Okounkov, Andrei; Olshanski, Grigori
1998
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
Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Zbl 0796.43005
Kerov, Serguei; Olshanski, Grigori; Vershik, Anatoli
1993
Point processes and the infinite symmetric group. Zbl 1044.20501
Borodin, Alexei; Olshanski, Grigori
1998
Markov processes on partitions. Zbl 1105.60052
Borodin, Alexei; Olshanski, Grigori
2006
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 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
Quantized universal enveloping superalgebra of type $$Q$$ and a super- extension of the Hecke algebra. Zbl 0766.17017
Ol’shanskij, G. I.
1992
Unitary representations of (G,K)-pairs connected with the infinite symmetric group S($$\infty)$$. Zbl 0731.20009
Ol’shanskij, G. I.
1990
Harmonic functions on multiplicative graphs and interpolation polynomials. Zbl 0939.05082
Borodin, Alexei; Olshanski, Grigori
2000
The ASEP and determinantal point processes. Zbl 1369.60031
Borodin, Alexei; Olshanski, Grigori
2017
Asymptotics of Plancherel-type random partitions. Zbl 1117.60051
Borodin, Alexei; Olshanski, Grigori
2007
$$Z$$-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
$$q$$-exchangeability via quasi-invariance. Zbl 1204.60029
Gnedin, Alexander; Olshanski, Grigori
2010
Infinite-dimensional diffusions as limits of random walks on partitions. Zbl 1163.60036
Borodin, Alexei; Olshanski, Grigori
2009
Stochastic dynamics related to Plancherel measure on partitions. Zbl 1109.60041
Borodin, Alexei; Olshanski, Grigori
2006
An introduction to harmonic analysis on the infinite symmetric group. Zbl 1035.05100
Olshanski, Grigori
2003
$$z$$-measures on partitions, Robinson-Schensted-Knuth correspondence, and $$\beta=2$$ random matrix ensembles. Zbl 0987.15013
Borodin, Alexei; Olshanski, Grigori
2001
Limits of $$BC$$-type orthogonal polynomials as the number of variables goes to infinity. Zbl 1151.33008
Okounkov, Andrei; Olshanski, Grigori
2006
Bethe subalgebras in twisted Yangians. Zbl 0876.17015
Nazarov, Maxim; Olshanski, Grigori
1996
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
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
The quasi-invariance property for the gamma kernel determinantal measure. Zbl 1218.60004
Olshanski, Grigori
2011
Meixner polynomials and random partitions. Zbl 1126.60006
Borodin, Alexei; Olshanski, Grigori
2006
Twisted Yangians and infinite-dimensional classical Lie algebras. Zbl 0780.17025
Ol’shanskiĭ, G. I.
1992
On semigroups related to infinite-dimensional groups. Zbl 0736.22014
Ol’shanskij, G. I.
1991
Unitary representations of infinite dimensional pairs (G,K) and the formalism of R. Howe. Zbl 0724.22020
Ol’shanskij, G. I.
1990
Giambelli compatible point processes. Zbl 1108.05093
Borodin, Alexei; Olshanski, Grigori; Strahov, Eugene
2006
Representation theory and random point processes. Zbl 1087.15025
Borodin, Alexei; Olshanski, Grigori
2005
Classification of irreducible representations of groups of automorphisms of Bruhat-Tits trees. Zbl 0371.22014
Ol’shanskii, G. I.
1977
Limit shapes for growing extreme characters of $$U(\infty)$$. Zbl 1325.60013
Borodin, Alexei; Bufetov, Alexey; Olshanski, Grigori
2015
A $$q$$-analogue of de Finetti’s theorem. Zbl 1200.60029
Gnedin, Alexander; Olshanski, Grigori
2009
Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. Zbl 0739.22015
Ol’shanskij, G. I.
1991
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
The two-sided infinite extension of the Mallows model for random permutations. Zbl 1242.60010
Gnedin, Alexander; Olshanski, Grigori
2012
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
Plancherel averages: remarks on a paper by Stanley. Zbl 1193.05161
Olshanski, Grigori
2010
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
Gorin, Vadim; Olshanski, Grigori
2016
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
New ”large” groups of type I. Zbl 0484.22027
Ol’shanskij, G. I.
1982
Multivariate Jacobi polynomials and the Selberg integral. Zbl 1306.43006
Olshanski, G. I.; Osinenko, A. A.
2012
Anisotropic Young diagrams and infinite-dimensional diffusion processes with the Jack parameter. Zbl 1193.60097
Olshanski, Grigori
2010
Centralizer construction for twisted Yangians. Zbl 1026.17021
Molev, Alexander; Olshanski, Grigori
2000
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
Infinite-dimensional classical groups of finite $$r$$-rank: description of representations and asymptotic theory. Zbl 0545.22020
Ol’shanskiĭ, G. I.
1984
Invariant orderings in simple Lie groups: Solution of a problem of Eh. B. Vinberg. Zbl 0576.32040
Ol’shanskij, G. I.
1983
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
Laguerre and Meixner orthogonal bases in the algebra of symmetric functions. Zbl 1257.33015
Olshanski, Grigori
2012
Difference operators and determinantal point processes. Zbl 1157.60319
Olshanski, Grigori
2008
The boundary of Eulerian number triangle. Zbl 1126.60065
Gnedin, Alexander; Olshanski, Grigori
2006
Point processes related to the infinite symmetric group. Zbl 1087.60041
Olshanski, Grigori
2003
Unitary representations of infinite-dimensional pairs $$(G,K)$$ and the formalism of R. Howe. Zbl 0532.22019
Ol’shanskiĭ, G. I.
1983
Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines. Zbl 1281.22003
Olshanski, Grigori
2013
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
Complex Lie semigroups, Hardy spaces and the Gel’fand-Gindikin program. Zbl 0789.22011
Ol’shanskij, G. I.
1991
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. Zbl 0709.43007
Nazarov, Maxime; Neretin, Yuriĭ; Olshanskiĭ, Grigoriĭ
1989
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
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
An analogue of the big $$q$$-Jacobi polynomials in the algebra of symmetric functions. Zbl 1381.33021
Olshanski, G. I.
2017
Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities. Zbl 1075.43009
Ol’shanskij, G. I.
2003
Random Young tableaux and combinatorial identities. Zbl 0982.05110
Olshanski, Grigori; Regev, Amitai
2001
Shifted Schur functions. Zbl 0894.05053
Okun’kov, A. Yu.; Ol’shanskij, G.
1997
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
Markov dynamics on the dual object to the infinite-dimensional unitary group. Zbl 1388.60134
Olshanski, Grigori
2016
Extended Gelfand-Tsetlin graph, its $$q$$-boundary, and $$q$$-B-splines. Zbl 1358.43009
Olshanski, G. I.
2016
The representation ring of the unitary groups and Markov processes of algebraic origin. Zbl 1359.22016
Olshanski, Grigori
2016
Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Zbl 0990.20005
Molev, A. I.; Olshanski, G. I.
2001
Weil representation and norms of Gaussian operators. Zbl 0848.22017
Ol’shanskij, G. I.
1994
Yangians and universal enveloping algebras. Zbl 0691.17005
Ol’shanskij, G. I.
1989
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
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
On the duality theorem of Frobenius. Zbl 0234.22012
Ol’shanskij, G. I.
1969
Multivariate Jacobi polynomials and the Selberg integral. II. Zbl 1347.43004
Olshanski, G.; Osinenko, A.
2016
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. Zbl 0790.43009
Olshanskiĭ, Grigori
1991
Irreducible unitary representations of the group U(p,q) admitting the limit q$$\to \infty$$. Zbl 0713.20043
Ol’shanskij, G. I.
1989
Determinantal point processes and fermion quasifree states. Zbl 07223233
Olshanski, Grigori
2020
The topological support of the z-measures on the Thoma simplex. Zbl 1422.43001
Olshanski, G. I.
2018
Diffusion processes on the Thoma cone. Zbl 1357.60085
Olshanski, G. I.
2016
Approximation of Markov dynamics on the dual object of the infinite-dimensional unitary group. Zbl 1343.60112
Olshanski, G. I.
2015
Determinantal point processes and fermion quasifree states. Zbl 07223233
Olshanski, Grigori
2020
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
Gorin, Vadim; Olshanski, Grigori
2016
Markov dynamics on the dual object to the infinite-dimensional unitary group. Zbl 1388.60134
Olshanski, Grigori
2016
Extended Gelfand-Tsetlin graph, its $$q$$-boundary, and $$q$$-B-splines. Zbl 1358.43009
Olshanski, G. I.
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
Determinantal measures related to big $$q$$-Jacobi polynomials. Zbl 1376.60016
Gorin, V. E.; Olshanski, G. I.
2015
Approximation of Markov dynamics on the dual object of the infinite-dimensional unitary group. Zbl 1343.60112
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
Multivariate Jacobi polynomials and the Selberg integral. Zbl 1306.43006
Olshanski, G. I.; Osinenko, A. A.
2012
Laguerre and Meixner orthogonal bases in the algebra of symmetric functions. Zbl 1257.33015
Olshanski, Grigori
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’shanskij, G. I.
2003
Kerov’s central limit theorem for the Plancherel measure on Young diagrams. Zbl 1016.05073
Ivanov, Vladimir; Olshanski, Grigori
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
Shifted Schur functions. Zbl 0894.05053
Okun’kov, A. Yu.; Ol’shanskij, 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’shanskij, G.
1996
Ergodic unitarily invariant measures on the space of infinite Hermitian matrices. Zbl 0853.22016
Ol’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’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’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’shanskij, G. I.
1992
Twisted Yangians and infinite-dimensional classical Lie algebras. Zbl 0780.17025
Ol’shanskiĭ, G. I.
1992
On semigroups related to infinite-dimensional groups. Zbl 0736.22014
Ol’shanskij, G. I.
1991
Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. Zbl 0739.22015
Ol’shanskij, G. I.
1991
Complex Lie semigroups, Hardy spaces and the Gel’fand-Gindikin program. Zbl 0789.22011
Ol’shanskij, G. I.
1991
Generalized characters of $$U(\infty)$$ and inner functions. Zbl 0790.43009
Olshanskiĭ, Grigori
1991
Unitary representations of (G,K)-pairs connected with the infinite symmetric group S($$\infty)$$. Zbl 0731.20009
Ol’shanskij, G. I.
1990
Unitary representations of infinite dimensional pairs (G,K) and the formalism of R. Howe. Zbl 0724.22020
Ol’shanskij, G. I.
1990
Semigroups generated by the Weil representation of the infinite-dimensional symplectic group. Zbl 0709.43007
Nazarov, Maxime; Neretin, Yuriĭ; Olshanskiĭ, Grigoriĭ
1989
Yangians and universal enveloping algebras. Zbl 0691.17005
Ol’shanskij, G. I.
1989
Irreducible unitary representations of the group U(p,q) admitting the limit q$$\to \infty$$. Zbl 0713.20043
Ol’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’shanskij, G. I.
1988
Method of holomorphic extensions in the theory of unitary representations of infinite-dimensional classical groups. Zbl 0668.22008
Ol’shanskij, G. I.
1988
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
Unitary representations of the infinite symmetric group: a semigroup approach. Zbl 0605.22005
Ol’shanskij, G. I.
1985
Infinite-dimensional classical groups of finite $$r$$-rank: description of representations and asymptotic theory. Zbl 0545.22020
Ol’shanskiĭ, G. I.
1984
Invariant orderings in simple Lie groups: Solution of a problem of Eh. B. Vinberg. Zbl 0576.32040
Ol’shanskij, G. I.
1983
Unitary representations of infinite-dimensional pairs $$(G,K)$$ and the formalism of R. Howe. Zbl 0532.22019
Ol’shanskiĭ, G. I.
1983
Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Zbl 0503.22011
Ol’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’shanskij, G. I.
1982
New ”large” groups of type I. Zbl 0484.22027
Ol’shanskij, G. I.
1982
Spherical functions and characters on the group $$U(\infty)^X$$. Zbl 0506.22021
Ol’shanskij, G. I.
1982
Spherical functions and characters on the group U(infinity)*. Zbl 0497.22023
Ol’shanskij, G. I.
1982
Description of unitary representations with highest weight for groups U(p,q). Zbl 0455.22004
Ol’shanskij, G. I.
1981
Description of unitary representations with highest weight for the groups U(p,q). Zbl 0439.22019
Ol’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’shanskij, G. I.
1979
...and 8 more Documents
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#### Cited by 729 Authors

 56 Borodin, Alexei 41 Ol’shanskiĭ, Grigoriĭ Iosifovich 24 Gorin, Vadim 24 Neretin, Yuriĭ Aleksandrovich 19 Molev, Alexander I. 17 Hilgert, Joachim 17 Neeb, Karl-Hermann 17 Vershik, Anatoliĭ Moiseevich 16 Bufetov, Aleksandr Igorevich 15 Petrov, Leonid 15 Ragoucy, Eric 13 Corwin, Ivan 12 Bufetov, Alekseĭ Igor’evich 11 Doikou, Anastasia 11 Okun’kov, Andreĭ Yur’evich 10 Crampé, Nicolas 10 Śniady, Piotr 9 Féray, Valentin 9 Fulman, Jason E. 9 Hofmann, Karl Heinrich 9 Nazarov, Maxim Leonidovich 9 Qiu, Yanqi 8 Assiotis, Theodoros 8 Kerov, Sergei V. 8 Lassalle, Michel 8 Strahov, Eugene 7 Frappat, Luc 7 Guay, Nicolas 6 Cuenca, Cesar 6 Ferrari, Patrik Lino 6 Kang, Seok-Jin 6 Lopushanski, Oleh V. 6 Matsumoto, Sho 6 Rains, Eric M. 6 Sergeev, Aleksandr Nikolaevich 5 Arnaudon, Daniel 5 Avan, Jean 5 Betea, Dan 5 Blower, Gordon 5 Gnedin, Alexander V. 5 Gorin, V. E. 5 Jing, Naihuan 5 Jung, Ji Hye 5 Khoroshkin, Sergey M. 5 Najnudel, Joseph 5 Nikeghbali, Ashkan 5 Ørsted, Bent 5 Regelskis, Vidas 5 Varchenko, Alexander Nikolaevich 5 Veselov, Alexander Petrovich 4 Adler, Mark 4 Brundan, Jonathan 4 Chicherin, Dmitry 4 Derkachëv, Sergeĭ Èduardovich 4 Diaconis, Persi Warren 4 Duits, Maurice 4 Forrester, Peter J. 4 Ghosal, Promit 4 Grantcharov, Dimitar 4 Han, Guo-Niu 4 Kim, Myungho 4 Kuan, Jeffrey 4 Kuhn, Maria Gabriella 4 Martínez-Finkelshtein, Andrei 4 Mironov, Andrei D. 4 Mukhin, Evgeny 4 Ólafsson, Gestur 4 Osinenko, A. A. 4 Panova, Greta 4 Regev, Amitai 4 Romik, Dan 4 Rybnikov, Leonid Grigor’evich 4 Tarasov, Vitaly Olegovich 4 van Moerbeke, Pierre 4 Warnaar, S. Ole 4 Webb, Christian 4 Yoo, Hyun Jae 3 Albeverio, Sergio A. 3 Barraquand, Guillaume 3 Beltiţă, Daniel 3 Benkart, Georgia M. 3 Bouali, Mohamed 3 Bouttier, Jérémie 3 Deift, Percy A. 3 Diaz, Pablo 3 Dołȩga, Maciej 3 Dörr, Norbert 3 Feĭgin, Boris L’vovich 3 Hivert, Florent 3 Hora, Akihito 3 Iorgov, Nikolai 3 Itoh, Minoru 3 Johansson, Kurt 3 Kleshchev, Alexander S. 3 Korotkikh, S. Yu. 3 Kozyrev, Sergeĭ Vladimirovich 3 Kuijlaars, Arno B. J. 3 Kvinge, Henry 3 Lawson, Jimmie Don 3 Le Doussal, Pierre ...and 629 more Authors
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#### Cited in 158 Serials

 55 Advances in Mathematics 37 Communications in Mathematical Physics 36 Journal of Mathematical Sciences (New York) 33 Functional Analysis and its Applications 27 Journal of Mathematical Physics 27 Journal of Functional Analysis 24 Journal of Algebra 21 Transactions of the American Mathematical Society 20 The Annals of Probability 19 Probability Theory and Related Fields 18 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 17 Letters in Mathematical Physics 17 Advances in Applied Mathematics 15 Nuclear Physics. B 14 Journal of Statistical Physics 14 Journal of High Energy Physics 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 12 Selecta Mathematica. New Series 11 Journal of Statistical Mechanics: Theory and Experiment 9 Electronic Journal of Probability 8 Inventiones Mathematicae 8 Journal of Combinatorial Theory. Series A 8 Mathematische Zeitschrift 8 Proceedings of the American Mathematical Society 7 Discrete Mathematics 7 Compositio Mathematica 7 Bulletin of the American Mathematical Society. New Series 6 Journal of Geometry and Physics 6 Journal of Approximation Theory 6 European Journal of Combinatorics 6 Journal of Theoretical Probability 6 Stochastic Processes and their Applications 6 Annales Henri Poincaré 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 Journal of the American Mathematical Society 5 Bernoulli 5 Séminaire Lotharingien de Combinatoire 5 Representation Theory 5 The Ramanujan Journal 4 Journal of Mathematical Analysis and Applications 4 Theoretical and Mathematical Physics 4 Arkiv för Matematik 4 Monatshefte für Mathematik 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Transformation Groups 4 Annals of Combinatorics 4 Proceedings of the Steklov Institute of Mathematics 3 Russian Mathematical Surveys 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 3 Random Matrices: Theory and Applications 2 International Journal of Modern Physics A 2 Communications in Algebra 2 Mathematical Notes 2 Reviews in Mathematical Physics 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 Statistics & Probability Letters 2 Physica D 2 Constructive Approximation 2 International Journal of Mathematics 2 Random Structures & Algorithms 2 The Annals of Applied Probability 2 Differential Geometry and its Applications 2 Geometric and Functional Analysis. GAFA 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Combinatorics, Probability and Computing 2 The Electronic Journal of Combinatorics 2 Electronic Communications in Probability 2 Sbornik: Mathematics 2 Abstract and Applied Analysis 2 Geometry & Topology 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 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Japanese Journal of Mathematics. 3rd Series 2 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Algebraic Combinatorics 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Problems of Information Transmission 1 Reports on Mathematical Physics 1 Theory of Probability and its Applications ...and 58 more Serials
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#### Cited in 52 Fields

 298 Probability theory and stochastic processes (60-XX) 222 Combinatorics (05-XX) 150 Topological groups, Lie groups (22-XX) 131 Nonassociative rings and algebras (17-XX) 123 Group theory and generalizations (20-XX) 116 Statistical mechanics, structure of matter (82-XX) 97 Quantum theory (81-XX) 87 Special functions (33-XX) 83 Abstract harmonic analysis (43-XX) 73 Linear and multilinear algebra; matrix theory (15-XX) 39 Dynamical systems and ergodic theory (37-XX) 39 Operator theory (47-XX) 37 Associative rings and algebras (16-XX) 37 Functional analysis (46-XX) 35 Algebraic geometry (14-XX) 24 Differential geometry (53-XX) 22 Partial differential equations (35-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 19 Measure and integration (28-XX) 18 Number theory (11-XX) 16 Statistics (62-XX) 13 Several complex variables and analytic spaces (32-XX) 13 Ordinary differential equations (34-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 10 Functions of a complex variable (30-XX) 9 Convex and discrete geometry (52-XX) 9 Manifolds and cell complexes (57-XX) 9 Global analysis, analysis on manifolds (58-XX) 7 Difference and functional equations (39-XX) 6 Numerical analysis (65-XX) 6 Relativity and gravitational theory (83-XX) 5 Approximations and expansions (41-XX) 4 Category theory; homological algebra (18-XX) 4 General topology (54-XX) 4 Biology and other natural sciences (92-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Integral transforms, operational calculus (44-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 $$K$$-theory (19-XX) 2 Potential theory (31-XX) 2 Algebraic topology (55-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX)