# zbMATH — the first resource for mathematics

## Kirillov, Alexander A. jun.

Compute Distance To:
 Author ID: kirillov.alexander-a-jun Published as: Kirillov, A.; Kirillov, A. A. jun.; Kirillov, A. jun.; Kirillov, Alexander A. jun.; Kirillov, Alexander jun.; Kirillov, Alexander jun. Homepage: http://www.math.stonybrook.edu/~kirillov/ External Links: MGP · Math-Net.Ru · Wikidata
 Documents Indexed: 30 Publications since 1989, including 5 Books
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#### Co-Authors

 11 single-authored 8 Etingof, Pavel Il’ich 4 Frenkel, Igor B. 2 Bakalov, Bojko 2 Onat, Emin Turan 2 Thind, J. 1 Boehler, Jean-Paul 1 Huang, Yi-Zhi 1 Khovanov, Mikhail G. 1 Lascoux, Alain 1 Lepowsky, James 1 Ostrik, Victor Valentinovich 1 Varchenko, Alexander Nikolaevich
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#### Serials

 3 Duke Mathematical Journal 2 Communications in Mathematical Physics 2 Functional Analysis and its Applications 2 Journal of Algebra 2 Transformation Groups 2 Cambridge Studies in Advanced Mathematics 1 Advances in Mathematics 1 Compositio Mathematica 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Journal of Elasticity 1 Bulletin of the American Mathematical Society. New Series 1 Mathematical Research Letters 1 Electronic Research Announcements of the American Mathematical Society 1 Advances in Theoretical and Mathematical Physics 1 Algebraic & Geometric Topology 1 Moscow Mathematical Journal 1 Graduate Studies in Mathematics 1 Mathematical Surveys and Monographs 1 University Lecture Series
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#### Fields

 20 Nonassociative rings and algebras (17-XX) 9 Combinatorics (05-XX) 8 Quantum theory (81-XX) 5 Category theory; homological algebra (18-XX) 5 Manifolds and cell complexes (57-XX) 4 Algebraic geometry (14-XX) 4 Associative rings and algebras (16-XX) 4 Group theory and generalizations (20-XX) 4 Special functions (33-XX) 3 Topological groups, Lie groups (22-XX) 2 Mechanics of deformable solids (74-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX)

#### Citations contained in zbMATH

26 Publications have been cited 814 times in 651 Documents Cited by Year
Lectures on tensor categories and modular functors. Zbl 0965.18002
Bakalov, B.; Kirillov, A. jun.
2001
On a $$q$$-analogue of the McKay correspondence and the ADE classification of $$\mathfrak{sl}_{2}$$ conformal field theories. Zbl 1024.17013
Kirillov, Alexander jun.; Ostrik, Viktor
2002
Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006
Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun.
1998
Braided tensor categories and extensions of vertex operator algebras. Zbl 1388.17014
Huang, Yi-Zhi; Kirillov, Alexander jun.; Lepowsky, James
2015
On an inner product in modular tensor categories. Zbl 0861.05065
Kirillov, Alexander A. jun.
1996
Macdonald’s polynomials and representations of quantum groups. Zbl 0833.17007
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1994
Spherical functions on affine Lie groups. Zbl 0848.43010
Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun.
1995
Kazhdan-Lusztig polynomials and canonical basis. Zbl 0918.17012
Frenkel, I. B.; Khovanov, M. G.; Kirillov, A. A. jun.
1998
Lectures on affine Hecke algebras and Macdonald’s conjectures. Zbl 0884.05100
Kirillov, Alexander A. jun.
1997
Representations of affine Lie algebras, parabolic differential equations, and Lamé functions. Zbl 0811.17026
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1994
On the polynomial invariants of the elasticity tensor. Zbl 0808.73007
Boehler, J. P.; Kirillov, A. A. jun.; Onat, E. T.
1994
Modular categories and orbifold models. Zbl 1073.17011
Kirillov, Alexander jun.
2002
An introduction to Lie groups and Lie algebras. Zbl 1153.17001
Kirillov, Alexander jun.
2008
On the Lego-Teichmüller game. Zbl 0999.57021
Bakalov, B.; Kirillov, A. jun.
2000
Quiver representations and quiver varieties. Zbl 1355.16002
Kirillov, Alexander jun.
2016
Representation-theoretic proof of the inner product and symmetry identities for Macdonald’s polynomials. Zbl 0859.17005
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1996
On Cherednik-Macdonald-Mehta identities. Zbl 0897.05089
Etingof, Pavel; Kirillov, Alexander jun.
1998
On the affine analogue of Jack and Macdonald polynomials. Zbl 0873.33011
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1995
A unified representation-theoretic approach to special functions. Zbl 0868.33010
Kirillov, A. A. jun.; Etingof, P. I.
1994
Factorization of Kazhdan-Lusztig elements for Grassmannians. Zbl 1002.20004
Kirillov, Alexander jun.; Lascoux, Alain
2000
An introduction to Lie groups and Lie algebras. Reprint of the 2008 hardback edition. Zbl 1360.22001
Kirillov, Alexander jun.
2017
Coxeter elements and periodic Auslander-Reiten quiver. Zbl 1231.20035
Kirillov, A.; Thind, J.
2010
On piecewise linear cell decompositions. Zbl 1283.57026
Kirillov, Alexander jun.
2012
On inner product in modular tensor categories. II: Inner product on conformal blocks and affine inner product identities. Zbl 0905.05084
Kirillov, Alexander A. jun.
1998
Canonical basis and homology of local systems. Zbl 0973.17016
Frenkel, Igor; Kirillov, Alexander jun.; Varchenko, Alexander
1997
McKay correspondence and equivariant sheaves on $$\mathbb P^1$$. Zbl 1171.14302
Kirillov, Alexander jun.
2006
An introduction to Lie groups and Lie algebras. Reprint of the 2008 hardback edition. Zbl 1360.22001
Kirillov, Alexander jun.
2017
Quiver representations and quiver varieties. Zbl 1355.16002
Kirillov, Alexander jun.
2016
Braided tensor categories and extensions of vertex operator algebras. Zbl 1388.17014
Huang, Yi-Zhi; Kirillov, Alexander jun.; Lepowsky, James
2015
On piecewise linear cell decompositions. Zbl 1283.57026
Kirillov, Alexander jun.
2012
Coxeter elements and periodic Auslander-Reiten quiver. Zbl 1231.20035
Kirillov, A.; Thind, J.
2010
An introduction to Lie groups and Lie algebras. Zbl 1153.17001
Kirillov, Alexander jun.
2008
McKay correspondence and equivariant sheaves on $$\mathbb P^1$$. Zbl 1171.14302
Kirillov, Alexander jun.
2006
On a $$q$$-analogue of the McKay correspondence and the ADE classification of $$\mathfrak{sl}_{2}$$ conformal field theories. Zbl 1024.17013
Kirillov, Alexander jun.; Ostrik, Viktor
2002
Modular categories and orbifold models. Zbl 1073.17011
Kirillov, Alexander jun.
2002
Lectures on tensor categories and modular functors. Zbl 0965.18002
Bakalov, B.; Kirillov, A. jun.
2001
On the Lego-Teichmüller game. Zbl 0999.57021
Bakalov, B.; Kirillov, A. jun.
2000
Factorization of Kazhdan-Lusztig elements for Grassmannians. Zbl 1002.20004
Kirillov, Alexander jun.; Lascoux, Alain
2000
Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006
Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun.
1998
Kazhdan-Lusztig polynomials and canonical basis. Zbl 0918.17012
Frenkel, I. B.; Khovanov, M. G.; Kirillov, A. A. jun.
1998
On Cherednik-Macdonald-Mehta identities. Zbl 0897.05089
Etingof, Pavel; Kirillov, Alexander jun.
1998
On inner product in modular tensor categories. II: Inner product on conformal blocks and affine inner product identities. Zbl 0905.05084
Kirillov, Alexander A. jun.
1998
Lectures on affine Hecke algebras and Macdonald’s conjectures. Zbl 0884.05100
Kirillov, Alexander A. jun.
1997
Canonical basis and homology of local systems. Zbl 0973.17016
Frenkel, Igor; Kirillov, Alexander jun.; Varchenko, Alexander
1997
On an inner product in modular tensor categories. Zbl 0861.05065
Kirillov, Alexander A. jun.
1996
Representation-theoretic proof of the inner product and symmetry identities for Macdonald’s polynomials. Zbl 0859.17005
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1996
Spherical functions on affine Lie groups. Zbl 0848.43010
Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun.
1995
On the affine analogue of Jack and Macdonald polynomials. Zbl 0873.33011
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1995
Macdonald’s polynomials and representations of quantum groups. Zbl 0833.17007
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1994
Representations of affine Lie algebras, parabolic differential equations, and Lamé functions. Zbl 0811.17026
Etingof, Pavel I.; Kirillov, Alexander A. jun.
1994
On the polynomial invariants of the elasticity tensor. Zbl 0808.73007
Boehler, J. P.; Kirillov, A. A. jun.; Onat, E. T.
1994
A unified representation-theoretic approach to special functions. Zbl 0868.33010
Kirillov, A. A. jun.; Etingof, P. I.
1994
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#### Cited by 678 Authors

 26 Runkel, Ingo 21 Rowell, Eric C. 19 Etingof, Pavel Il’ich 18 Schweigert, Christoph 17 Creutzig, Thomas 17 Fuchs, Jürgen 16 Wang, Zhenghan 14 Kong, Liang 13 Varchenko, Alexander Nikolaevich 10 Dong, Chongying 10 Kirillov, Alexander A. jun. 9 Davydov, Alekseĭ Aleksandrovich 9 Ng, Siu-Hung 8 Bruillard, Paul 8 Galindo Martínez, César Neyit 8 Ostrik, Victor Valentinovich 8 Plavnik, Julia Yael 8 Shimizu, Kenichi 7 Cox, Ben Lewis 7 Fehér, László Gy. 7 Huang, Yi-Zhi 7 Naaijkens, Pieter 7 Nikshych, Dmitri 7 Olive, Marc 7 Stokman, Jasper V. 6 Coquereaux, Robert 6 Frenkel, Igor B. 6 Kanade, Shashank 6 Lam, Ching Hung 6 Lin, Xingjun 6 Ridout, David 6 Schopieray, Andrew 5 Andersen, Jørgen Ellegaard 5 Brenti, Francesco 5 Burciu, Sebastian M. 5 Carqueville, Nils 5 Kolev, Boris 5 Li, Haisheng 5 Linshaw, Andrew Ross 5 Snyder, Noah 4 Auffray, Nicolas 4 Bonderson, Parsa 4 Cohen, Miriam 4 Fehér, László M. 4 Felder, Giovanni 4 Futorny, Vyacheslav M. 4 Gainutdinov, Azat M. 4 Gawȩdzki, Krzysztof 4 Gelaki, Shlomo 4 Gustafson, Paul P. 4 Jones, Corey 4 Kawahigashi, Yasuyuki 4 Langmann, Edwin 4 Li, Libin 4 Naidu, Deepak 4 Natale, Sonia 4 Pusztai, Béla Gábor 4 Reshetikhin, Nikolai Yu. 4 Schaumann, Gregor 4 Semikhatov, Alexei M. 4 Sun, Yi 4 van Diejen, Jan Felipe 4 Westreich, Sara 4 Zinn-Justin, Paul 3 Arakawa, Tomoyuki 3 Auffray, Nicole 3 Auger, Jean-Claude 3 Bantay, Peter 3 Bischoff, Marcel 3 Boyarchenko, Mitya 3 Brundan, Jonathan 3 Chalykh, Oleg A. 3 Cherednik, Ivan V. 3 de Gier, Jan 3 Desmorat, Boris 3 Drinfeld, Vladimir Gershonovich 3 Fjelstad, Jens 3 Funar, Louis 3 Gao, Yun 3 Grossman, Pinhas 3 Jiao, Xiangyu 3 Jurisich, Elizabeth 3 Kamnitzer, Joel 3 Kholodenko, Arkady L. 3 Khovanov, Mikhail G. 3 Kujawa, Jonathan R. 3 Le, Thang Tu Quoc 3 Mackaay, Marco 3 Martins, Renato Alessandro 3 Müger, Michael 3 Oblomkov, Alexei A. 3 Penneys, David 3 Pinzari, Claudia 3 Qi, Liqun 3 Rains, Eric M. 3 Razumov, Alexander V. 3 Rehren, Karl-Henning 3 Sakhnovych, Lev Aronovych 3 Sawin, Stephen F. 3 Schauenburg, Peter ...and 578 more Authors
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#### Cited in 109 Serials

 76 Communications in Mathematical Physics 60 Journal of Algebra 51 Advances in Mathematics 32 Journal of Mathematical Physics 23 Nuclear Physics. B 23 Journal of High Energy Physics 21 Letters in Mathematical Physics 19 Selecta Mathematica. New Series 17 Journal of Pure and Applied Algebra 13 Proceedings of the American Mathematical Society 12 Journal of Geometry and Physics 12 Duke Mathematical Journal 12 Journal of Knot Theory and its Ramifications 11 Algebras and Representation Theory 10 Transactions of the American Mathematical Society 9 Reviews in Mathematical Physics 9 Mathematische Zeitschrift 9 Communications in Contemporary Mathematics 9 Algebraic & Geometric Topology 8 Transformation Groups 8 Quantum Topology 7 Communications in Algebra 7 Journal of the American Mathematical Society 7 Annals of Physics 7 Journal of Elasticity 7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Theoretical and Mathematical Physics 6 Compositio Mathematica 6 Bulletin of the American Mathematical Society. New Series 6 Representation Theory 5 Journal of Algebraic Combinatorics 4 Inventiones Mathematicae 4 International Journal of Mathematics 3 Journal of Statistical Physics 3 Glasgow Mathematical Journal 3 Journal of Combinatorial Theory. Series A 3 Journal of Functional Analysis 3 Monatshefte für Mathematik 3 Pacific Journal of Mathematics 3 Advances in Applied Mathematics 3 Applied Categorical Structures 3 Mathematics and Mechanics of Solids 3 Acta Mathematica Sinica. English Series 3 Annales Henri Poincaré 3 Journal of Noncommutative Geometry 2 International Journal of Modern Physics A 2 Israel Journal of Mathematics 2 Journal of Mathematical Analysis and Applications 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Topology and its Applications 2 European Journal of Combinatorics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Experimental Mathematics 2 Theory and Applications of Categories 2 The Ramanujan Journal 2 Geometry & Topology 2 Foundations of Computational Mathematics 2 Central European Journal of Mathematics 2 Journal of Statistical Mechanics: Theory and Experiment 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 International Journal of Engineering Science 1 Journal of the Mechanics and Physics of Solids 1 Periodica Mathematica Hungarica 1 Russian Mathematical Surveys 1 Acta Mathematica 1 The Annals of Probability 1 Archiv der Mathematik 1 Automatica 1 Canadian Journal of Mathematics 1 Commentarii Mathematici Helvetici 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Differential Equations 1 Memoirs of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Studies in Applied Mathematics 1 Theoretical Computer Science 1 Tohoku Mathematical Journal. Second Series 1 Science in China. Series A 1 Random Structures & Algorithms 1 Continuum Mechanics and Thermodynamics 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Calculus of Variations and Partial Differential Equations 1 Algebra Colloquium 1 Journal of Lie Theory 1 Electronic Research Announcements of the American Mathematical Society 1 The Journal of Fourier Analysis and Applications 1 Documenta Mathematica 1 Journal of Group Theory 1 Annals of Combinatorics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Nonlinear Mathematical Physics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Quantum Information Processing 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Algebra and its Applications 1 Frontiers of Mathematics in China 1 International Electronic Journal of Algebra (IEJA) ...and 9 more Serials
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#### Cited in 45 Fields

 252 Quantum theory (81-XX) 239 Nonassociative rings and algebras (17-XX) 192 Category theory; homological algebra (18-XX) 115 Associative rings and algebras (16-XX) 109 Group theory and generalizations (20-XX) 72 Manifolds and cell complexes (57-XX) 53 Algebraic geometry (14-XX) 48 Special functions (33-XX) 46 Functional analysis (46-XX) 38 Combinatorics (05-XX) 36 Topological groups, Lie groups (22-XX) 30 Differential geometry (53-XX) 30 Statistical mechanics, structure of matter (82-XX) 23 Dynamical systems and ergodic theory (37-XX) 22 Several complex variables and analytic spaces (32-XX) 22 Global analysis, analysis on manifolds (58-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 15 Mechanics of deformable solids (74-XX) 14 Partial differential equations (35-XX) 12 Number theory (11-XX) 12 Commutative algebra (13-XX) 12 Relativity and gravitational theory (83-XX) 10 Algebraic topology (55-XX) 9 Mechanics of particles and systems (70-XX) 8 Difference and functional equations (39-XX) 7 Probability theory and stochastic processes (60-XX) 6 $$K$$-theory (19-XX) 6 Ordinary differential equations (34-XX) 5 Functions of a complex variable (30-XX) 5 Abstract harmonic analysis (43-XX) 4 Computer science (68-XX) 3 Approximations and expansions (41-XX) 3 Operator theory (47-XX) 2 Field theory and polynomials (12-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Numerical analysis (65-XX) 2 Fluid mechanics (76-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

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