Edit Profile (opens in new tab) Kirillov, Alexander A. jun. Co-Author Distance Author ID: kirillov.alexander-a-jun Published as: Kirillov, Alexander jun.; Kirillov, Alexander A. jun.; Kirillov, A. A. jun.; Kirillov, A. jun.; Kirillov, Alexander jun.; Kirillov, A. more...less Homepage: http://www.math.stonybrook.edu/~kirillov/ External Links: MGP · Wikidata · Math-Net.Ru Documents Indexed: 33 Publications since 1989, including 5 Books 2 Contributions as Editor Co-Authors: 13 Co-Authors with 20 Joint Publications 416 Co-Co-Authors all top 5 Co-Authors 12 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 Bott, Raoul Harry 1 Gani, Vakhid A. 1 Huang, Yi-Zhi 1 Khokhlov, Andreĭ Vladimirovich 1 Khovanov, Mikhail G. 1 Lascoux, Alain 1 Lepowsky, James 1 Ostrik, Victor Valentinovich 1 Rubin, Sergey G. 1 Tham, Ying Hong 1 Tu, Loring W. 1 Varchenko, Alexander Nikolaevich 1 Voronov, Theodore 1 Warner, Frank W. all top 5 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 Journal of Cosmology and Astroparticle Physics 1 Fixed Point Theory 1 Graduate Studies in Mathematics 1 Mathematical Surveys and Monographs 1 University Lecture Series 1 Quantum Topology all top 5 Fields 20 Nonassociative rings and algebras (17-XX) 9 Combinatorics (05-XX) 8 Quantum theory (81-XX) 7 Manifolds and cell complexes (57-XX) 6 Category theory; homological algebra (18-XX) 4 Algebraic geometry (14-XX) 4 Associative rings and algebras (16-XX) 4 Group theory and generalizations (20-XX) 4 Topological groups, Lie groups (22-XX) 4 Special functions (33-XX) 2 Algebraic topology (55-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of deformable solids (74-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 31 Publications have been cited 1,081 times in 863 Documents Cited by ▼ Year ▼ Lectures on tensor categories and modular functors. Zbl 0965.18002Bakalov, B.; Kirillov, A. jun. 352 2001 On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories. Zbl 1024.17013Kirillov, Alexander jun.; Ostrik, Viktor 135 2002 Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 109 1998 Braided tensor categories and extensions of vertex operator algebras. Zbl 1388.17014Huang, Yi-Zhi; Kirillov, Alexander jun.; Lepowsky, James 87 2015 On an inner product in modular tensor categories. Zbl 0861.05065Kirillov, Alexander A. jun. 44 1996 Macdonald’s polynomials and representations of quantum groups. Zbl 0833.17007Etingof, Pavel I.; Kirillov, Alexander A. jun. 35 1994 Modular categories and orbifold models. Zbl 1073.17011Kirillov, Alexander jun. 34 2002 On the polynomial invariants of the elasticity tensor. Zbl 0808.73007Boehler, J. P.; Kirillov, A. A. jun.; Onat, E. T. 30 1994 Spherical functions on affine Lie groups. Zbl 0848.43010Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 29 1995 Kazhdan-Lusztig polynomials and canonical basis. Zbl 0918.17012Frenkel, I. B.; Khovanov, M. G.; Kirillov, A. A. jun. 28 1998 Lectures on affine Hecke algebras and Macdonald’s conjectures. Zbl 0884.05100Kirillov, Alexander A. jun. 28 1997 An introduction to Lie groups and Lie algebras. Zbl 1153.17001Kirillov, Alexander jun. 27 2008 On the Lego-Teichmüller game. Zbl 0999.57021Bakalov, B.; Kirillov, A. jun. 24 2000 Representations of affine Lie algebras, parabolic differential equations, and Lamé functions. Zbl 0811.17026Etingof, Pavel I.; Kirillov, Alexander A. jun. 23 1994 Quiver representations and quiver varieties. Zbl 1355.16002Kirillov, Alexander jun. 22 2016 Representation-theoretic proof of the inner product and symmetry identities for Macdonald’s polynomials. Zbl 0859.17005Etingof, Pavel I.; Kirillov, Alexander A. jun. 12 1996 On the affine analogue of Jack and Macdonald polynomials. Zbl 0873.33011Etingof, Pavel I.; Kirillov, Alexander A. jun. 11 1995 On Cherednik-Macdonald-Mehta identities. Zbl 0897.05089Etingof, Pavel; Kirillov, Alexander jun. 10 1998 A unified representation-theoretic approach to special functions. Zbl 0868.33010Kirillov, A. A. jun.; Etingof, P. I. 8 1994 Factorization of Kazhdan-Lusztig elements for Grassmannians. Zbl 1002.20004Kirillov, Alexander jun.; Lascoux, Alain 7 2000 An introduction to Lie groups and Lie algebras. Reprint of the 2008 hardback edition. Zbl 1360.22001Kirillov, Alexander jun. 7 2017 On piecewise linear cell decompositions. Zbl 1283.57026Kirillov, Alexander jun. 5 2012 Coxeter elements and periodic Auslander-Reiten quiver. Zbl 1231.20035Kirillov, A.; Thind, J. 5 2010 Foundations of differentiable manifolds and Lie groups. (Osnovy teorii gladkikh mnogoobrazij i grupp Li). Transl. from the English by F. F. Voronov and A. V. Khokhlov. Transl. ed. and with a preface by A. A. Kirillov. (Osnovy teorii gladkikh mnogoobrazij i grupp Li.) Zbl 0691.58005Warner, Frank W. 4 1987 On inner product in modular tensor categories. II: Inner product on conformal blocks and affine inner product identities. Zbl 0905.05084Kirillov, Alexander A. jun. 3 1998 Classical transitions with the topological number changing in the early universe. Zbl 07458878Gani, Vakhid A.; Kirillov, Alexander A.; Rubin, Sergey G. 2 2018 McKay correspondence and equivariant sheaves on \(\mathbb P^1\). Zbl 1171.14302Kirillov, Alexander jun. 2 2006 Canonical basis and homology of local systems. Zbl 0973.17016Frenkel, Igor; Kirillov, Alexander jun.; Varchenko, Alexander 2 1997 Differential forms in algebraic topology. Transl. from the English by I. V. Savel’ev and G. S. Shmelev. Transl. ed. by A. A. Kirillov. (Дифференциальные формы в алгебраической топологии.) Zbl 0675.55002Bott, Raoul; Tu, Loring W. 1 1989 Coxeter elements and root bases. Zbl 1281.17013Kirillov, A. jun.; Thind, J. 1 2011 Factorization homology and 4D TQFT. Zbl 1498.57029Kirillov, Alexander jun.; Tham, Ying Hong 1 2022 Factorization homology and 4D TQFT. Zbl 1498.57029Kirillov, Alexander jun.; Tham, Ying Hong 1 2022 Classical transitions with the topological number changing in the early universe. Zbl 07458878Gani, Vakhid A.; Kirillov, Alexander A.; Rubin, Sergey G. 2 2018 An introduction to Lie groups and Lie algebras. Reprint of the 2008 hardback edition. Zbl 1360.22001Kirillov, Alexander jun. 7 2017 Quiver representations and quiver varieties. Zbl 1355.16002Kirillov, Alexander jun. 22 2016 Braided tensor categories and extensions of vertex operator algebras. Zbl 1388.17014Huang, Yi-Zhi; Kirillov, Alexander jun.; Lepowsky, James 87 2015 On piecewise linear cell decompositions. Zbl 1283.57026Kirillov, Alexander jun. 5 2012 Coxeter elements and root bases. Zbl 1281.17013Kirillov, A. jun.; Thind, J. 1 2011 Coxeter elements and periodic Auslander-Reiten quiver. Zbl 1231.20035Kirillov, A.; Thind, J. 5 2010 An introduction to Lie groups and Lie algebras. Zbl 1153.17001Kirillov, Alexander jun. 27 2008 McKay correspondence and equivariant sheaves on \(\mathbb P^1\). Zbl 1171.14302Kirillov, Alexander jun. 2 2006 On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories. Zbl 1024.17013Kirillov, Alexander jun.; Ostrik, Viktor 135 2002 Modular categories and orbifold models. Zbl 1073.17011Kirillov, Alexander jun. 34 2002 Lectures on tensor categories and modular functors. Zbl 0965.18002Bakalov, B.; Kirillov, A. jun. 352 2001 On the Lego-Teichmüller game. Zbl 0999.57021Bakalov, B.; Kirillov, A. jun. 24 2000 Factorization of Kazhdan-Lusztig elements for Grassmannians. Zbl 1002.20004Kirillov, Alexander jun.; Lascoux, Alain 7 2000 Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 109 1998 Kazhdan-Lusztig polynomials and canonical basis. Zbl 0918.17012Frenkel, I. B.; Khovanov, M. G.; Kirillov, A. A. jun. 28 1998 On Cherednik-Macdonald-Mehta identities. Zbl 0897.05089Etingof, Pavel; Kirillov, Alexander jun. 10 1998 On inner product in modular tensor categories. II: Inner product on conformal blocks and affine inner product identities. Zbl 0905.05084Kirillov, Alexander A. jun. 3 1998 Lectures on affine Hecke algebras and Macdonald’s conjectures. Zbl 0884.05100Kirillov, Alexander A. jun. 28 1997 Canonical basis and homology of local systems. Zbl 0973.17016Frenkel, Igor; Kirillov, Alexander jun.; Varchenko, Alexander 2 1997 On an inner product in modular tensor categories. Zbl 0861.05065Kirillov, Alexander A. jun. 44 1996 Representation-theoretic proof of the inner product and symmetry identities for Macdonald’s polynomials. Zbl 0859.17005Etingof, Pavel I.; Kirillov, Alexander A. jun. 12 1996 Spherical functions on affine Lie groups. Zbl 0848.43010Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 29 1995 On the affine analogue of Jack and Macdonald polynomials. Zbl 0873.33011Etingof, Pavel I.; Kirillov, Alexander A. jun. 11 1995 Macdonald’s polynomials and representations of quantum groups. Zbl 0833.17007Etingof, Pavel I.; Kirillov, Alexander A. jun. 35 1994 On the polynomial invariants of the elasticity tensor. Zbl 0808.73007Boehler, J. P.; Kirillov, A. A. jun.; Onat, E. T. 30 1994 Representations of affine Lie algebras, parabolic differential equations, and Lamé functions. Zbl 0811.17026Etingof, Pavel I.; Kirillov, Alexander A. jun. 23 1994 A unified representation-theoretic approach to special functions. Zbl 0868.33010Kirillov, A. A. jun.; Etingof, P. I. 8 1994 Differential forms in algebraic topology. Transl. from the English by I. V. Savel’ev and G. S. Shmelev. Transl. ed. by A. A. Kirillov. (Дифференциальные формы в алгебраической топологии.) Zbl 0675.55002Bott, Raoul; Tu, Loring W. 1 1989 Foundations of differentiable manifolds and Lie groups. (Osnovy teorii gladkikh mnogoobrazij i grupp Li). Transl. from the English by F. F. Voronov and A. V. Khokhlov. Transl. ed. and with a preface by A. A. Kirillov. (Osnovy teorii gladkikh mnogoobrazij i grupp Li.) Zbl 0691.58005Warner, Frank W. 4 1987 all cited Publications top 5 cited Publications all top 5 Cited by 886 Authors 30 Creutzig, Thomas 28 Runkel, Ingo 27 Rowell, Eric C. 27 Schweigert, Christoph 20 Fuchs, Jürgen 19 Etingof, Pavel Il’ich 19 Varchenko, Alexander Nikolaevich 18 Wang, Zhenghan 16 Kong, Liang 15 Ng, Siu-Hung 12 Dong, Chongying 11 Kirillov, Alexander A. jun. 11 Olive, Marc 11 Plavnik, Julia Yael 10 Davydov, Alekseĭ Aleksandrovich 10 Fehér, László Gy. 10 Galindo Martínez, César Neyit 10 McRae, Robert 10 Stokman, Jasper V. 9 Bruillard, Paul 9 Kolev, Boris 9 Yang, Jinwei 8 Desmorat, Boris 8 Huang, Yi-Zhi 8 Nikshych, Dmitri 8 Ostrik, Victor Valentinovich 8 Shimizu, Kenichi 8 van Diejen, Jan Felipe 7 Cox, Ben Lewis 7 Desmorat, Rodrigue 7 Kanade, Shashank 7 Lin, Xingjun 7 Linshaw, Andrew Ross 7 Naaijkens, Pieter 7 Schopieray, Andrew 7 Snyder, Noah 7 Zhang, Qing 6 Andersen, Jørgen Ellegaard 6 Burciu, Sebastian M. 6 Coquereaux, Robert 6 Frenkel, Igor B. 6 Jones, Corey 6 Kawahigashi, Yasuyuki 6 Lam, Ching Hung 6 Razumov, Alexander V. 6 Reshetikhin, Nikolai Yu. 6 Ridout, David 5 Bonderson, Parsa 5 Brenti, Francesco 5 Carqueville, Nils 5 Felder, Giovanni 5 Gustafson, Paul P. 5 Li, Haisheng 5 Naidu, Deepak 5 Schaumann, Gregor 5 Vlaar, Bart 5 Walton, Chelsea 5 Wang, Yilong 5 Zheng, Hao 4 Arakawa, Tomoyuki 4 Bischoff, Marcel 4 Cohen, Miriam 4 Douglas, Christopher L. 4 Evans, David E. 4 Futorny, Vyacheslav M. 4 Gainutdinov, Azat M. 4 Gannon, Terry 4 Gawȩdzki, Krzysztof 4 Gelaki, Shlomo 4 Jiao, Xiangyu 4 Johnson-Freyd, Theo 4 Lacabanne, Abel 4 Langmann, Edwin 4 Li, Libin 4 Mackaay, Marco 4 Natale, Sonia 4 Penneys, David 4 Pusztai, Béla Gábor 4 Ren, Li 4 Rimányi, Richárd 4 Schauenburg, Peter 4 Semikhatov, Alexei M. 4 Sun, Yi 4 Westreich, Sara 4 Xu, Feng 4 Zinn-Justin, Paul 3 Andruskiewitsch, Nicolás 3 Auffray, Nicolas 3 Auger, Jean-Claude 3 Bantay, Peter 3 Boyarchenko, Mitya 3 Brundan, Jonathan 3 Buican, Matthew 3 Chalykh, Oleg A. 3 Cherednik, Ivan V. 3 Cuenca, Cesar 3 Cui, Shawn Xingshan 3 de Gier, Jan 3 Dong, Jingcheng 3 Drinfeld, Vladimir Gershonovich ...and 786 more Authors all top 5 Cited in 144 Serials 105 Communications in Mathematical Physics 74 Journal of Algebra 62 Advances in Mathematics 39 Journal of High Energy Physics 33 Journal of Mathematical Physics 30 Letters in Mathematical Physics 26 Nuclear Physics. B 25 Selecta Mathematica. New Series 22 Journal of Pure and Applied Algebra 15 Proceedings of the American Mathematical Society 15 Journal of Knot Theory and its Ramifications 14 Algebras and Representation Theory 13 Journal of Geometry and Physics 13 Transactions of the American Mathematical Society 12 Duke Mathematical Journal 11 Reviews in Mathematical Physics 11 Mathematische Zeitschrift 11 Communications in Contemporary Mathematics 11 Algebraic & Geometric Topology 10 Communications in Algebra 10 Transformation Groups 10 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Quantum Topology 8 Journal of Elasticity 7 Theoretical and Mathematical Physics 7 Compositio Mathematica 7 Journal of the American Mathematical Society 7 Annals of Physics 7 Bulletin of the American Mathematical Society. New Series 7 Journal of Physics A: Mathematical and Theoretical 6 Inventiones Mathematicae 6 Journal of Algebraic Combinatorics 6 Representation Theory 5 International Journal of Mathematics 5 Mathematics and Mechanics of Solids 5 Journal of Algebra and its Applications 4 Journal of Statistical Physics 4 Journal of Functional Analysis 3 Canadian Journal of Mathematics 3 Glasgow Mathematical Journal 3 Journal of Combinatorial Theory. Series A 3 Monatshefte für Mathematik 3 Pacific Journal of Mathematics 3 Proceedings of the London Mathematical Society. Third Series 3 Topology and its Applications 3 Advances in Applied Mathematics 3 Indagationes Mathematicae. New Series 3 Applied Categorical Structures 3 Theory and Applications of Categories 3 The Ramanujan Journal 3 Acta Mathematica Sinica. English Series 3 Annales Henri Poincaré 3 Foundations of Computational Mathematics 3 Journal of Noncommutative Geometry 3 Arnold Mathematical Journal 2 International Journal of Modern Physics A 2 International Journal of Engineering Science 2 Israel Journal of Mathematics 2 Journal of Mathematical Analysis and Applications 2 Russian Mathematical Surveys 2 Journal of the London Mathematical Society. Second Series 2 Memoirs of the American Mathematical Society 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 European Journal of Combinatorics 2 IMRN. International Mathematics Research Notices 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Experimental Mathematics 2 Journal of Lie Theory 2 Geometry & Topology 2 Central European Journal of Mathematics 2 Journal of Statistical Mechanics: Theory and Experiment 2 Japanese Journal of Mathematics. 3rd Series 2 Analysis and Mathematical Physics 1 International Journal of Modern Physics B 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 Journal of the Mechanics and Physics of Solids 1 Mathematical Notes 1 Periodica Mathematica Hungarica 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Archiv der Mathematik 1 Automatica 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Indiana University Mathematics Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Differential Equations 1 Journal of the Mathematical Society of Japan 1 Manuscripta Mathematica 1 Mathematische Annalen 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 Tôhoku Mathematical Journal. Second Series 1 Ergodic Theory and Dynamical Systems ...and 44 more Serials all top 5 Cited in 48 Fields 346 Quantum theory (81-XX) 320 Nonassociative rings and algebras (17-XX) 277 Category theory; homological algebra (18-XX) 159 Associative rings and algebras (16-XX) 138 Group theory and generalizations (20-XX) 100 Manifolds and cell complexes (57-XX) 73 Algebraic geometry (14-XX) 64 Special functions (33-XX) 54 Functional analysis (46-XX) 52 Combinatorics (05-XX) 44 Differential geometry (53-XX) 42 Topological groups, Lie groups (22-XX) 39 Statistical mechanics, structure of matter (82-XX) 32 Several complex variables and analytic spaces (32-XX) 28 Global analysis, analysis on manifolds (58-XX) 27 Dynamical systems and ergodic theory (37-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 23 Number theory (11-XX) 23 Mechanics of deformable solids (74-XX) 21 Commutative algebra (13-XX) 19 Algebraic topology (55-XX) 19 Relativity and gravitational theory (83-XX) 14 Partial differential equations (35-XX) 12 Mechanics of particles and systems (70-XX) 11 \(K\)-theory (19-XX) 11 Probability theory and stochastic processes (60-XX) 10 Difference and functional equations (39-XX) 8 Ordinary differential equations (34-XX) 8 Abstract harmonic analysis (43-XX) 7 Functions of a complex variable (30-XX) 6 Computer science (68-XX) 4 Numerical analysis (65-XX) 3 Field theory and polynomials (12-XX) 3 Approximations and expansions (41-XX) 3 Operator theory (47-XX) 3 Convex and discrete geometry (52-XX) 3 Information and communication theory, circuits (94-XX) 2 Geometry (51-XX) 2 Statistics (62-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 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.