Edit Profile (opens in new tab) Frenkel, Igor B. Co-Author Distance Author ID: frenkel.igor-b Published as: Frenkel, Igor B.; Frenkel, Igor; Frenkel, I. B.; Frenkel’, I. B.; Frenkel, I. more...less Further Spellings: Френкель Игорь Борисович Homepage: https://users.math.yale.edu/public_html/People/frenkel.html External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 75 Publications since 1980, including 4 Books and 3 Additional arXiv Preprints Biographic References: 2 Publications Co-Authors: 46 Co-Authors with 67 Joint Publications 1,479 Co-Co-Authors all top 5 Co-Authors 7 single-authored 8 Lepowsky, James 7 Libine, Matvei 7 Meurman, Arne 5 Feingold, Alex Jay 5 Jing, Naihuan 5 Khovanov, Mikhail G. 4 Kirillov, Alexander A. jun. 4 Wang, Weiqiang 3 Etingof, Pavel Il’ich 3 Ries, John F. X. 3 Zeitlin, Anton M. 2 Ding, Jintai 2 Jardim, Marcos 2 Kim, Hyun Kyu 2 Malkin, Anton Z. 2 Reshetikhin, Nikolai Yu. 2 Stroppel, Catharina H. 2 Turaev, Vladimir Georgievich 2 Vybornov, Maxim 1 Beck, Jonathan 1 Benkart, Georgia McClure 1 Bernstein, Joseph 1 Crane, Louis 1 Duncan, John F. R. 1 Feĭgin, Boris L’vovich 1 Finkelberg, Michael Vladlenovich 1 Huang, Yi-Zhi 1 Ip, Ivan Chi-Ho 1 Kac, Victor 1 Kang, Seok-Jin 1 Khesin, Boris A. 1 Lee, Hyeonmi 1 Malikov, Fyodor 1 Moore, Gregory Winthrop 1 Penkov, Ivan B. 1 Penner, Robert C. 1 Rybnikov, Leonid Grigor’evich 1 Savage, Alistair 1 Schiffmann, Olivier G. 1 Serganova, Vera V. 1 Styrkas, Konstantin 1 Sussan, Joshua 1 Todorov, Andrey N. 1 Varchenko, Alexander Nikolaevich 1 Zhu, Minxian 1 Zhu, Yongchang all top 5 Serials 11 Communications in Mathematical Physics 7 IMRN. International Mathematics Research Notices 6 Advances in Mathematics 5 Duke Mathematical Journal 4 Selecta Mathematica. New Series 3 Journal of Algebra 3 Proceedings of the National Academy of Sciences of the United States of America 2 Inventiones Mathematicae 2 Advances in Theoretical and Mathematical Physics 1 Journal of Mathematical Physics 1 Compositio Mathematica 1 Functional Analysis and its Applications 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of Functional Analysis 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 International Journal of Mathematics 1 Transformation Groups 1 Contemporary Mathematics 1 Mathematical Surveys and Monographs 1 Pure and Applied Mathematics (Academic Press) 1 Journal of Noncommutative Geometry 1 Communications in Number Theory and Physics 1 Quantum Topology all top 5 Fields 59 Nonassociative rings and algebras (17-XX) 28 Quantum theory (81-XX) 14 Group theory and generalizations (20-XX) 12 Topological groups, Lie groups (22-XX) 8 Functions of a complex variable (30-XX) 7 Associative rings and algebras (16-XX) 6 Number theory (11-XX) 5 Algebraic geometry (14-XX) 5 Special functions (33-XX) 5 Manifolds and cell complexes (57-XX) 4 Combinatorics (05-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Category theory; homological algebra (18-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Partial differential equations (35-XX) 3 Statistical mechanics, structure of matter (82-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 66 Publications have been cited 3,990 times in 2,471 Documents Cited by ▼ Year ▼ Vertex operator algebras and the monster. Zbl 0674.17001 Frenkel, Igor; Lepowsky, James; Meurman, Arne 846 1988 On axiomatic approaches to vertex operator algebras and modules. Zbl 0789.17022 Frenkel, Igor B.; Huang, Yi-Zhi; Lepowsky, James 419 1993 Vertex operator algebras associated to representations of affine and Virasoro algebras. Zbl 0848.17032 Frenkel, Igor B.; Zhu, Yongchang 412 1992 Basic representations of affine Lie algebras and dual resonance models. Zbl 0493.17010 Frenkel, I. B.; Kac, V. G. 266 1980 Quantum affine algebras and holonomic difference equations. Zbl 0760.17006 Frenkel, I. B.; Reshetikhin, N. Yu. 220 1992 A natural representation of the Fischer-Griess monster with the modular function J as character. Zbl 0543.20016 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 124 1984 Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006 Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 121 1998 Vertex representations of quantum affine algebras. Zbl 0662.17006 Frenkel, Igor B.; Jing, Naihuan 111 1988 Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases. Zbl 0892.57014 Crane, Louis; Frenkel, Igor B. 103 1994 Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory. Zbl 0479.17003 Frenkel, I. B. 95 1981 Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\). Zbl 0786.17008 Ding, Jintai; Frenkel, Igor B. 92 1993 Spinor construction of vertex operator algebras, triality, and \(E_ 8^{(1)}\). Zbl 0743.17029 Feingold, Alex J.; Frenkel, Igor B.; Ries, John F. X. 89 1991 A categorification of the Temperley-Lieb algebra and Schur quotients of \(U(\mathfrak{sl}_2)\) via projective and Zuckerman functors. Zbl 0981.17001 Bernstein, Joseph; Frenkel, Igor; Khovanov, Mikhail 84 1999 Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. Zbl 0974.17016 Frenkel, Igor B.; Turaev, Vladimir G. 70 1997 Canonical bases in tensor products and graphical calculus for \(U_ q(sl_ 2)\). Zbl 0883.17013 Frenkel, Igor B.; Khovanov, Mikhail G. 67 1997 Classical affine algebras. Zbl 0601.17012 Feingold, Alex J.; Frenkel, Igor B. 65 1985 A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2. Zbl 0489.17008 Feingold, Alex J.; Frenkel, Igor B. 51 1983 A categorification of finite-dimensional irreducible representations of quantum \({\mathfrak{sl}_2}\) and their tensor products. Zbl 1188.17011 Frenkel, Igor; Khovanov, Mikhail; Stroppel, Catharina 49 2006 Spinor representations of affine Lie algebras. Zbl 0451.17004 Frenkel, I. B. 47 1980 Orbital theory for affine Lie algebras. Zbl 0548.17007 Frenkel, I. B. 41 1984 A moonshine module for the monster. Zbl 0556.17008 Frenkel, Igor B.; Lepowsky, James; Meurman, Arne 38 1985 Representations of Kac-Moody algebras and dual resonance models. Zbl 0558.17013 Frenkel, I. B. 34 1985 Rademacher sums, moonshine and gravity. Zbl 1279.11045 Duncan, John F. R.; Frenkel, Igor B. 33 2011 Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols. Zbl 1256.17006 Frenkel, Igor B.; Stroppel, Catharina; Sussan, Joshua 30 2012 Vertex representations via finite groups and the McKay correspondence. Zbl 1011.17020 Frenkel, Igor B.; Jing, Naihuan; Wang, Weiqiang 29 2000 Spherical functions on affine Lie groups. Zbl 0848.43010 Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 29 1995 Kazhdan-Lusztig polynomials and canonical basis. Zbl 0918.17012 Frenkel, I. B.; Khovanov, M. G.; Kirillov, A. A. jun. 28 1998 Vertex operator calculus. Zbl 0657.17010 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 28 1987 Representations of affine Lie algebras, Hecke modular forms and Korteweg- de Vries type equations. Zbl 0505.17008 Frenkel, I. B. 27 1982 Quaternionic analysis, representation theory and physics. Zbl 1167.30030 Frenkel, Igor; Libine, Matvei 26 2008 An introduction to the Monster. Zbl 0648.20030 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 24 1986 Split quaternionic analysis and separation of the series for \(\mathrm{SL}(2,\mathbb R)\) and \(\mathrm{SL}(2,\mathbb C)/\mathrm{SL}(2,\mathbb R)\). Zbl 1264.30037 Frenkel, Igor; Libine, Matvei 22 2011 Central extensions of current groups in two dimensions. Zbl 0822.22014 Etingof, Pavel I.; Frenkel, Igor B. 21 1994 Level 1 perfect crystals and path realizations of basic representations at \(q=0\). Zbl 1149.17016 Benkart, Georgia; Frenkel, Igor; Kang, Seokjin; Lee, Hyeonmi 19 2006 Introduction from the book “Algebras of vertex operators and the Monster”. Zbl 0759.20001 Frenkel, I.; Lepowsky, J.; Meurman, A. 18 1991 Affine Lie algebras and tame quivers. Zbl 1002.16012 Frenkel, Igor; Malkin, Anton; Vybornov, Maxim 17 2001 Quantum vertex representations via finite groups and the McKay correspondence. Zbl 1011.17011 Frenkel, Igor B.; Jing, Naihuan; Wang, Weiqiang 16 2000 Complex ADHM equations and sheaves on \(\mathbb P ^3\). Zbl 1145.14017 Frenkel, Igor B.; Jardim, Marcos 15 2008 Positive representations of split real quantum groups and future perspectives. Zbl 1381.17009 Frenkel, Igor B.; Ip, Ivan C. H. 13 2014 Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology. Zbl 1208.17021 Frenkel, Igor B.; Styrkas, Konstantin 12 2006 Bases of representations of type \(A\) affine Lie algebras via quiver varieties and statistical mechanics. Zbl 1023.17010 Frenkel, Igor B.; Savage, Alistair 12 2003 Quantum Teichmüller space from the quantum plane. Zbl 1271.30020 Frenkel, Igor B.; Kim, Hyun Kyu 12 2012 Simplex equations and their solutions. Zbl 0749.17039 Frenkel, Igor; Moore, Gregory 11 1991 A categorification of the boson-fermion correspondence via representation theory of \(sl(\infty)\). Zbl 1355.17032 Frenkel, Igor; Penkov, Ivan; Serganova, Vera 9 2016 Annihilating ideals and tilting functors. Zbl 0942.17017 Frenkel’, I. B.; Malikov, F. G. 8 1999 Spinor and oscillator representations of quantum groups. Zbl 0847.17013 Ding, Jintai; Frenkel, Igor B. 8 1994 Vertex algebras associated to modified regular representations of the Virasoro algebra. Zbl 1256.17011 Frenkel, Igor; Zhu, Minxian 8 2012 Virasoro algebra and wreath product convolution. Zbl 0981.17021 Frenkel, Igor B.; Wang, Weiqiang 7 2001 Twisted vertex representations via spin groups and the McKay correspondence. Zbl 1100.17502 Frenkel, Igor B.; Jing, Naihuan; Wang, Weiqiang 7 2002 Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces. Zbl 1285.14011 Feigin, Boris; Finkelberg, Michael; Frenkel, Igor; Rybnikov, Leonid 7 2011 Complex counterpart of Chern-Simons-Witten theory and holomorphic linking. Zbl 1135.32021 Frenkel, Igor B.; Todorov, Andrey N. 6 2007 Anti de Sitter deformation of quaternionic analysis and the second-order pole. Zbl 1318.30080 Frenkel, Igor; Libine, Matvei 6 2015 Quantum group as semi-infinite cohomology. Zbl 1196.81148 Frenkel, Igor B.; Zeitlin, Anton M. 5 2010 Representations of hyperbolic Kac-Moody algebras. Zbl 0795.17032 Feingold, Alex J.; Frenkel, Igor B.; Ries, John F. X. 4 1993 Four dimensional realization of two dimensional current groups. Zbl 0858.22017 Frenkel, Igor B.; Khesin, Boris A. 4 1996 Canonical basis and Macdonald polynomials. Zbl 0924.17006 Beck, Jonathan; Frenkel, Igor B.; Jing, Naihuan 4 1998 Homological realization of Nakajima varieties and Weyl group actions. Zbl 1095.17002 Frenkel, Igor; Khovanov, Mikhail; Schiffmann, Olivier 3 2005 Quantum instantons with classical moduli spaces. Zbl 1034.58025 Frenkel, Igor B.; Jardim, Marcos 3 2003 Quantum affine algebras, commutative systems of difference equations and elliptic solutions to the Yang-Baxter equations. Zbl 0818.17011 Frenkel, I. B.; Reshetikhin, N. Yu. 3 1992 Trigonometric solutions of the Yang-Baxter equation, nets, and hypergeometric functions. Zbl 0864.57024 Frenkel, Igor B.; Turaev, Vladimir G. 3 1995 Canonical basis and homology of local systems. Zbl 0973.17016 Frenkel, Igor; Kirillov, Alexander jun.; Varchenko, Alexander 2 1997 Sketch of a program for automorphic functions from universal Teichmüller theory to capture monstrous moonshine. Zbl 1497.11103 Frenkel, Igor; Penner, Robert 2 2022 Beyond affine Lie algebras. Zbl 0668.17016 Frenkel, I. B. 2 1987 Quantum group \(\mathrm{GL}_q(2)\) and quantum Laplace operator via semi-infinite cohomology. Zbl 1330.17017 Frenkel, Igor B.; Zeitlin, Anton M. 1 2013 On the continuous series for \(\widehat{sl(2,\mathbb R)}\). Zbl 1369.17019 Frenkel, Igor B.; Zeitlin, Anton M. 1 2014 Quaternionic analysis and the Schrödinger model for the minimal representation of \(O(3,3)\). Zbl 1261.30005 Frenkel, Igor; Libine, Matvei 1 2012 Sketch of a program for automorphic functions from universal Teichmüller theory to capture monstrous moonshine. Zbl 1497.11103 Frenkel, Igor; Penner, Robert 2 2022 A categorification of the boson-fermion correspondence via representation theory of \(sl(\infty)\). Zbl 1355.17032 Frenkel, Igor; Penkov, Ivan; Serganova, Vera 9 2016 Anti de Sitter deformation of quaternionic analysis and the second-order pole. Zbl 1318.30080 Frenkel, Igor; Libine, Matvei 6 2015 Positive representations of split real quantum groups and future perspectives. Zbl 1381.17009 Frenkel, Igor B.; Ip, Ivan C. H. 13 2014 On the continuous series for \(\widehat{sl(2,\mathbb R)}\). Zbl 1369.17019 Frenkel, Igor B.; Zeitlin, Anton M. 1 2014 Quantum group \(\mathrm{GL}_q(2)\) and quantum Laplace operator via semi-infinite cohomology. Zbl 1330.17017 Frenkel, Igor B.; Zeitlin, Anton M. 1 2013 Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols. Zbl 1256.17006 Frenkel, Igor B.; Stroppel, Catharina; Sussan, Joshua 30 2012 Quantum Teichmüller space from the quantum plane. Zbl 1271.30020 Frenkel, Igor B.; Kim, Hyun Kyu 12 2012 Vertex algebras associated to modified regular representations of the Virasoro algebra. Zbl 1256.17011 Frenkel, Igor; Zhu, Minxian 8 2012 Quaternionic analysis and the Schrödinger model for the minimal representation of \(O(3,3)\). Zbl 1261.30005 Frenkel, Igor; Libine, Matvei 1 2012 Rademacher sums, moonshine and gravity. Zbl 1279.11045 Duncan, John F. R.; Frenkel, Igor B. 33 2011 Split quaternionic analysis and separation of the series for \(\mathrm{SL}(2,\mathbb R)\) and \(\mathrm{SL}(2,\mathbb C)/\mathrm{SL}(2,\mathbb R)\). Zbl 1264.30037 Frenkel, Igor; Libine, Matvei 22 2011 Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces. Zbl 1285.14011 Feigin, Boris; Finkelberg, Michael; Frenkel, Igor; Rybnikov, Leonid 7 2011 Quantum group as semi-infinite cohomology. Zbl 1196.81148 Frenkel, Igor B.; Zeitlin, Anton M. 5 2010 Quaternionic analysis, representation theory and physics. Zbl 1167.30030 Frenkel, Igor; Libine, Matvei 26 2008 Complex ADHM equations and sheaves on \(\mathbb P ^3\). Zbl 1145.14017 Frenkel, Igor B.; Jardim, Marcos 15 2008 Complex counterpart of Chern-Simons-Witten theory and holomorphic linking. Zbl 1135.32021 Frenkel, Igor B.; Todorov, Andrey N. 6 2007 A categorification of finite-dimensional irreducible representations of quantum \({\mathfrak{sl}_2}\) and their tensor products. Zbl 1188.17011 Frenkel, Igor; Khovanov, Mikhail; Stroppel, Catharina 49 2006 Level 1 perfect crystals and path realizations of basic representations at \(q=0\). Zbl 1149.17016 Benkart, Georgia; Frenkel, Igor; Kang, Seokjin; Lee, Hyeonmi 19 2006 Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology. Zbl 1208.17021 Frenkel, Igor B.; Styrkas, Konstantin 12 2006 Homological realization of Nakajima varieties and Weyl group actions. Zbl 1095.17002 Frenkel, Igor; Khovanov, Mikhail; Schiffmann, Olivier 3 2005 Bases of representations of type \(A\) affine Lie algebras via quiver varieties and statistical mechanics. Zbl 1023.17010 Frenkel, Igor B.; Savage, Alistair 12 2003 Quantum instantons with classical moduli spaces. Zbl 1034.58025 Frenkel, Igor B.; Jardim, Marcos 3 2003 Twisted vertex representations via spin groups and the McKay correspondence. Zbl 1100.17502 Frenkel, Igor B.; Jing, Naihuan; Wang, Weiqiang 7 2002 Affine Lie algebras and tame quivers. Zbl 1002.16012 Frenkel, Igor; Malkin, Anton; Vybornov, Maxim 17 2001 Virasoro algebra and wreath product convolution. Zbl 0981.17021 Frenkel, Igor B.; Wang, Weiqiang 7 2001 Vertex representations via finite groups and the McKay correspondence. Zbl 1011.17020 Frenkel, Igor B.; Jing, Naihuan; Wang, Weiqiang 29 2000 Quantum vertex representations via finite groups and the McKay correspondence. Zbl 1011.17011 Frenkel, Igor B.; Jing, Naihuan; Wang, Weiqiang 16 2000 A categorification of the Temperley-Lieb algebra and Schur quotients of \(U(\mathfrak{sl}_2)\) via projective and Zuckerman functors. Zbl 0981.17001 Bernstein, Joseph; Frenkel, Igor; Khovanov, Mikhail 84 1999 Annihilating ideals and tilting functors. Zbl 0942.17017 Frenkel’, I. B.; Malikov, F. G. 8 1999 Lectures on representation theory and Knizhnik-Zamolodchikov equations. Zbl 0903.17006 Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 121 1998 Kazhdan-Lusztig polynomials and canonical basis. Zbl 0918.17012 Frenkel, I. B.; Khovanov, M. G.; Kirillov, A. A. jun. 28 1998 Canonical basis and Macdonald polynomials. Zbl 0924.17006 Beck, Jonathan; Frenkel, Igor B.; Jing, Naihuan 4 1998 Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. Zbl 0974.17016 Frenkel, Igor B.; Turaev, Vladimir G. 70 1997 Canonical bases in tensor products and graphical calculus for \(U_ q(sl_ 2)\). Zbl 0883.17013 Frenkel, Igor B.; Khovanov, Mikhail G. 67 1997 Canonical basis and homology of local systems. Zbl 0973.17016 Frenkel, Igor; Kirillov, Alexander jun.; Varchenko, Alexander 2 1997 Four dimensional realization of two dimensional current groups. Zbl 0858.22017 Frenkel, Igor B.; Khesin, Boris A. 4 1996 Spherical functions on affine Lie groups. Zbl 0848.43010 Etingof, Pavel I.; Frenkel, Igor B.; Kirillov, Alexander A. jun. 29 1995 Trigonometric solutions of the Yang-Baxter equation, nets, and hypergeometric functions. Zbl 0864.57024 Frenkel, Igor B.; Turaev, Vladimir G. 3 1995 Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases. Zbl 0892.57014 Crane, Louis; Frenkel, Igor B. 103 1994 Central extensions of current groups in two dimensions. Zbl 0822.22014 Etingof, Pavel I.; Frenkel, Igor B. 21 1994 Spinor and oscillator representations of quantum groups. Zbl 0847.17013 Ding, Jintai; Frenkel, Igor B. 8 1994 On axiomatic approaches to vertex operator algebras and modules. Zbl 0789.17022 Frenkel, Igor B.; Huang, Yi-Zhi; Lepowsky, James 419 1993 Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\). Zbl 0786.17008 Ding, Jintai; Frenkel, Igor B. 92 1993 Representations of hyperbolic Kac-Moody algebras. Zbl 0795.17032 Feingold, Alex J.; Frenkel, Igor B.; Ries, John F. X. 4 1993 Vertex operator algebras associated to representations of affine and Virasoro algebras. Zbl 0848.17032 Frenkel, Igor B.; Zhu, Yongchang 412 1992 Quantum affine algebras and holonomic difference equations. Zbl 0760.17006 Frenkel, I. B.; Reshetikhin, N. Yu. 220 1992 Quantum affine algebras, commutative systems of difference equations and elliptic solutions to the Yang-Baxter equations. Zbl 0818.17011 Frenkel, I. B.; Reshetikhin, N. Yu. 3 1992 Spinor construction of vertex operator algebras, triality, and \(E_ 8^{(1)}\). Zbl 0743.17029 Feingold, Alex J.; Frenkel, Igor B.; Ries, John F. X. 89 1991 Introduction from the book “Algebras of vertex operators and the Monster”. Zbl 0759.20001 Frenkel, I.; Lepowsky, J.; Meurman, A. 18 1991 Simplex equations and their solutions. Zbl 0749.17039 Frenkel, Igor; Moore, Gregory 11 1991 Vertex operator algebras and the monster. Zbl 0674.17001 Frenkel, Igor; Lepowsky, James; Meurman, Arne 846 1988 Vertex representations of quantum affine algebras. Zbl 0662.17006 Frenkel, Igor B.; Jing, Naihuan 111 1988 Vertex operator calculus. Zbl 0657.17010 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 28 1987 Beyond affine Lie algebras. Zbl 0668.17016 Frenkel, I. B. 2 1987 An introduction to the Monster. Zbl 0648.20030 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 24 1986 Classical affine algebras. Zbl 0601.17012 Feingold, Alex J.; Frenkel, Igor B. 65 1985 A moonshine module for the monster. Zbl 0556.17008 Frenkel, Igor B.; Lepowsky, James; Meurman, Arne 38 1985 Representations of Kac-Moody algebras and dual resonance models. Zbl 0558.17013 Frenkel, I. B. 34 1985 A natural representation of the Fischer-Griess monster with the modular function J as character. Zbl 0543.20016 Frenkel, I. B.; Lepowsky, J.; Meurman, A. 124 1984 Orbital theory for affine Lie algebras. Zbl 0548.17007 Frenkel, I. B. 41 1984 A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2. Zbl 0489.17008 Feingold, Alex J.; Frenkel, Igor B. 51 1983 Representations of affine Lie algebras, Hecke modular forms and Korteweg- de Vries type equations. Zbl 0505.17008 Frenkel, I. B. 27 1982 Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory. Zbl 0479.17003 Frenkel, I. B. 95 1981 Basic representations of affine Lie algebras and dual resonance models. Zbl 0493.17010 Frenkel, I. B.; Kac, V. G. 266 1980 Spinor representations of affine Lie algebras. Zbl 0451.17004 Frenkel, I. B. 47 1980 all cited Publications top 5 cited Publications all top 5 Cited by 1,759 Authors 74 Dong, Chongying 71 Li, Haisheng 70 Jing, Naihuan 57 Lam, Ching Hung 41 Huang, Yi-Zhi 32 Tan, Shaobin 30 Adamović, Dražen 30 Creutzig, Thomas 30 Mason, Geoffrey 30 Varchenko, Alexander Nikolaevich 29 Jiang, Cuipo 28 Frenkel, Igor B. 28 Linshaw, Andrew Ross 28 Wang, Qing 26 Milas, Antun 25 Kac, Victor 25 Yamada, Hiromichi 23 Arakawa, Tomoyuki 22 Mazorchuk, Volodymyr 21 Misra, Kailash C. 21 Yang, Jinwei 20 Lepowsky, James 19 Khovanov, Mikhail G. 17 Duncan, John F. R. 17 Kožić, Slaven 17 Shimakura, Hiroki 17 Zuevsky, Alexander 16 Miyamoto, Masahiko 16 Stroppel, Catharina H. 16 Tarasov, Vitaly Olegovich 16 Yamauchi, Hiroshi 15 Lauda, Aaron D. 15 McRae, Robert 15 Tuite, Michael P. 15 Wang, Weiqiang 14 Barron, Katrina 14 Feĭgin, Boris L’vovich 14 Frenkel, Edward V. 14 Kang, Seok-Jin 13 Chen, Fulin 13 Etingof, Pavel Il’ich 13 Lin, Xingjun 13 Ren, Li 13 Reshetikhin, Nikolai Yu. 13 Sussan, Joshua 13 Zhang, Yaozhong 12 Abe, Toshiyuki 12 Griess, Robert L. jun. 12 Perše, Ozren 12 Schlosser, Michael J. 12 Stokman, Jasper V. 12 Xu, Feng 12 Xu, Xiaoping 12 Yamskulna, Gaywalee 12 Yu, Nina 12 Zhang, Honglian 11 Anguelova, Iana I. 11 Cheng, Miranda C. N. 11 Gao, Yun 11 Pakuliak, Stanislav Z. 11 Ridout, David 11 Zinn-Justin, Paul 10 Cox, Ben Lewis 10 Futorny, Vyacheslav M. 10 Guo, Hongyan 10 Jurisich, Elizabeth 10 Kong, Liang 10 Lin, Zongzhu 10 Mu, Qiang 10 Qi, You 10 Spiridonov, Vyacheslav Pavlovich 10 Tsymbaliuk, Oleksandr 9 Butorac, Marijana 9 Calinescu, Corina 9 Cautis, Sabin 9 Harrison, Sarah M. 9 Harvey, Jeffrey A. 9 Ip, Ivan Chi-Ho 9 Jiao, Xiangyu 9 Jimbo, Michio 9 Kanade, Shashank 9 Kojima, Takeo 9 Kong, Fei 9 Kwon, Jae-Hoon 9 Molev, Alexander I. 9 Moore, Gregory Winthrop 9 Okado, Masato 9 Primc, Mirko 9 Savage, Alistair 9 Tanabe, Kenichiro 9 Warnaar, S. Ole 9 Zeitlin, Anton M. 8 Bantay, Peter 8 Bringmann, Kathrin 8 Brundan, Jonathan 8 Fehér, László Gy. 8 Gould, Mark D. 8 Hu, Naihong 8 Jardim, Marcos 8 Kirillov, Alexander A. jun. ...and 1,659 more Authors all top 5 Cited in 230 Serials 298 Journal of Algebra 255 Communications in Mathematical Physics 139 Advances in Mathematics 123 Journal of Mathematical Physics 107 Journal of High Energy Physics 99 Journal of Pure and Applied Algebra 82 Letters in Mathematical Physics 71 Communications in Algebra 61 Nuclear Physics. B 61 Transactions of the American Mathematical Society 46 Communications in Contemporary Mathematics 44 Duke Mathematical Journal 38 Journal of Geometry and Physics 38 Selecta Mathematica. New Series 34 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 30 Mathematische Zeitschrift 27 Theoretical and Mathematical Physics 26 Transformation Groups 25 Proceedings of the American Mathematical Society 23 Algebras and Representation Theory 22 Journal of Functional Analysis 22 International Journal of Mathematics 20 Journal of Physics A: Mathematical and Theoretical 19 The Ramanujan Journal 19 Journal of Algebra and its Applications 16 International Journal of Modern Physics A 16 Inventiones Mathematicae 16 Publications of the Research Institute for Mathematical Sciences, Kyoto University 15 Journal of Mathematical Sciences (New York) 15 Quantum Topology 14 Compositio Mathematica 14 Bulletin of the American Mathematical Society. New Series 14 Representation Theory 14 Journal of Statistical Mechanics: Theory and Experiment 14 Frontiers of Mathematics in China 13 Reviews in Mathematical Physics 13 Journal of Algebraic Combinatorics 13 Annales Henri Poincaré 11 Mathematische Annalen 11 Memoirs of the American Mathematical Society 10 Functional Analysis and its Applications 10 Science China. Mathematics 9 Journal of Knot Theory and its Ramifications 9 Advances in Applied Clifford Algebras 9 Algebraic & Geometric Topology 9 Central European Journal of Mathematics 8 Journal of Combinatorial Theory. Series A 8 Algebra Colloquium 8 Research in the Mathematical Sciences 7 Advances in Applied Mathematics 7 Acta Applicandae Mathematicae 7 Journal of the American Mathematical Society 7 Annals of Physics 6 Journal of the Mathematical Society of Japan 6 Journal of Soviet Mathematics 6 European Journal of Combinatorics 6 Journal of Lie Theory 6 Journal of the Institute of Mathematics of Jussieu 6 Japanese Journal of Mathematics. 3rd Series 5 Israel Journal of Mathematics 5 Journal of the London Mathematical Society. Second Series 5 Journal of Number Theory 5 Indagationes Mathematicae. New Series 5 Acta Mathematica Sinica. English Series 5 Forum of Mathematics, Sigma 4 Journal of Statistical Physics 4 Linear and Multilinear Algebra 4 Acta Mathematica 4 Bulletin of the London Mathematical Society 4 Glasgow Mathematical Journal 4 Journal für die Reine und Angewandte Mathematik 4 Nagoya Mathematical Journal 4 Science in China. Series A 4 St. Petersburg Mathematical Journal 4 Séminaire Lotharingien de Combinatoire 4 Geometry & Topology 4 Journal of the European Mathematical Society (JEMS) 4 Algebra & Number Theory 4 Arnold Mathematical Journal 3 Modern Physics Letters A 3 International Journal of Modern Physics B 3 Journal of Mathematical Analysis and Applications 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Physics Letters. B 3 Canadian Journal of Mathematics 3 Publications Mathématiques 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of Approximation Theory 3 Michigan Mathematical Journal 3 Proceedings of the Japan Academy. Series A 3 Constructive Approximation 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Experimental Mathematics 3 Annals of Combinatorics 3 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 3 Advances in Mathematical Physics 3 Analysis and Mathematical Physics 3 Journal de l’École Polytechnique – Mathématiques 2 Computers & Mathematics with Applications 2 Discrete Mathematics ...and 130 more Serials all top 5 Cited in 55 Fields 1,719 Nonassociative rings and algebras (17-XX) 906 Quantum theory (81-XX) 262 Group theory and generalizations (20-XX) 246 Associative rings and algebras (16-XX) 188 Number theory (11-XX) 183 Algebraic geometry (14-XX) 180 Category theory; homological algebra (18-XX) 160 Combinatorics (05-XX) 139 Special functions (33-XX) 134 Topological groups, Lie groups (22-XX) 114 Statistical mechanics, structure of matter (82-XX) 106 Manifolds and cell complexes (57-XX) 83 Relativity and gravitational theory (83-XX) 75 Dynamical systems and ergodic theory (37-XX) 73 Global analysis, analysis on manifolds (58-XX) 64 Differential geometry (53-XX) 57 Partial differential equations (35-XX) 56 Several complex variables and analytic spaces (32-XX) 51 Functional analysis (46-XX) 43 Functions of a complex variable (30-XX) 37 Linear and multilinear algebra; matrix theory (15-XX) 30 Algebraic topology (55-XX) 29 Commutative algebra (13-XX) 27 Probability theory and stochastic processes (60-XX) 26 Difference and functional equations (39-XX) 25 Information and communication theory, circuits (94-XX) 21 \(K\)-theory (19-XX) 11 Ordinary differential equations (34-XX) 11 Geometry (51-XX) 10 Operator theory (47-XX) 9 Abstract harmonic analysis (43-XX) 9 Statistics (62-XX) 8 Computer science (68-XX) 7 Convex and discrete geometry (52-XX) 7 Mechanics of particles and systems (70-XX) 6 Field theory and polynomials (12-XX) 6 Measure and integration (28-XX) 6 Numerical analysis (65-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 5 Approximations and expansions (41-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Mathematical logic and foundations (03-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 2 Fluid mechanics (76-XX) 1 General algebraic systems (08-XX) 1 Real functions (26-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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