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## Frenkel, Edward V.

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 Author ID: frenkel.edward-v Published as: Frenkel, Edward; Frenkel, E.; Frenkel, Edward V.; Frenkel’, E. V.; Frenkel’, Edward V.; Frenkel, E. V. External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 100 Publications since 1988, including 7 Books 1 Contribution as Editor Reviewing Activity: 4 Reviews
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#### Co-Authors

 23 single-authored 21 Feĭgin, Boris L’vovich 11 Gaitsgory, Dennis 5 Reshetikhin, Nikolai Yu. 4 Ben-Zvi, David 4 Hernandez, David 3 Mukhin, Evgeny 3 Szenes, András 3 Teleman, Constantin 3 Vilonen, Kari 2 Averina, Ya. S. 2 Enriquez, Benjamin 2 Kac, Victor G. 2 Kazhdan, David A. 2 Losev, Andrei S. 2 Myasnikov, Alexei G. 2 Ngô Bao Châu 2 Remeslennikov, Vladimir Nikanorovich 2 Rybnikov, Leonid Grigor’evich 2 Szczesny, Matthew 2 Zhu, Xinwen 1 Aganagic, Mina 1 Alekseev, Anton Yu. 1 Arakawa, Tomoyuki 1 Etingof, Pavel Il’ich 1 Gaiotto, Davide 1 Givental, Alexander Borisovich 1 Gross, Benedict Hyman 1 Gukov, Sergei 1 Langlands, Robert Phelan 1 Milanov, Todor E. 1 Nekrasov, Nikita Alexandrovich 1 Okun’kov, Andreĭ Yur’evich 1 Radul, Andrey 1 Rosso, Marc 1 Semenov-Tyan-Shanskiĭ, Mikhail Arsen’evich 1 Teschner, Jörg 1 Toledano Laredo, Valerio 1 Tolland, A. J. 1 Wakimoto, Minoru 1 Wang, Weiqiang 1 Webster, Ben 1 Witten, Edward 1 Yakimov, Milen T.
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#### Serials

 14 Communications in Mathematical Physics 5 Advances in Mathematics 5 Duke Mathematical Journal 4 IMRN. International Mathematics Research Notices 3 Letters in Mathematical Physics 3 Journal of the American Mathematical Society 3 Bulletin of the American Mathematical Society. New Series 3 Annals of Mathematics. Second Series 2 Physics Letters. B 2 Compositio Mathematica 2 Mathematical Research Letters 2 Mathematical Surveys and Monographs 2 Communications in Number Theory and Physics 1 International Journal of Modern Physics A 1 Mathematical Notes 1 Russian Mathematical Surveys 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Annales des Sciences Mathématiques du Québec 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Mathematische Annalen 1 Transactions of the Moscow Mathematical Society 1 Journal of the Ramanujan Mathematical Society 1 Notices of the American Mathematical Society 1 Journal of Algebraic Geometry 1 Journal of Mathematical Sciences (New York) 1 Selecta Mathematica. New Series 1 Representation Theory 1 Vestnik Omskogo Universiteta 1 Journal of High Energy Physics 1 Moscow Mathematical Journal 1 Journal of the Institute of Mathematics of Jussieu 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Pure and Applied Mathematics Quarterly 1 Cambridge Studies in Advanced Mathematics 1 Functional Analysis and Other Mathematics 1 Bulletin of Mathematical Sciences
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#### Fields

 65 Nonassociative rings and algebras (17-XX) 44 Quantum theory (81-XX) 33 Algebraic geometry (14-XX) 27 Topological groups, Lie groups (22-XX) 22 Number theory (11-XX) 15 Dynamical systems and ergodic theory (37-XX) 8 Partial differential equations (35-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 History and biography (01-XX) 6 Group theory and generalizations (20-XX) 4 General and overarching topics; collections (00-XX) 3 Differential geometry (53-XX) 2 Associative rings and algebras (16-XX) 2 $$K$$-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 2 Probability theory and stochastic processes (60-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX)

#### Citations contained in zbMATH Open

91 Publications have been cited 2,106 times in 1,184 Documents Cited by Year
Vertex algebras and algebraic curves. 2nd revised and expanded ed. Zbl 1106.17035
Frenkel, Edward; Ben-Zvi, David
2004
The $$q$$-characters of representations of quantum affine algebras and deformations of $$W$$-algebras. Zbl 0973.17015
Frenkel, Edward; Reshetikhin, Nicolai
1999
Vertex algebras and algebraic curves. Zbl 0981.17022
Frenkel, Edward; Ben-Zvi, David
2001
Quantization of the Drinfel’d-Sokolov reduction. Zbl 1242.17023
Feigin, Boris; Frenkel, Edward
1990
Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras. Zbl 0925.17022
Feigin, Boris; Frenkel, Edward
1992
Gaudin model, Bethe ansatz and critical level. Zbl 0812.35103
Feigin, Boris; Frenkel, Edward; Reshetikhin, Nikolai
1994
Characters and fusion rules for $$W$$-algebras via quantized Drinfeld- Sokolov reduction. Zbl 0768.17008
Frenkel, Edward; Kac, Victor; Wakimoto, Minoru
1992
Combinatorics of $$q$$-characters of finite-dimensional representations of quantum affine algebras. Zbl 1051.17013
Frenkel, Edward; Mukhin, Evgeny
2001
Affine Kac-Moody algebras and semi-infinite flag manifolds. Zbl 0722.17019
Feigin, Boris L.; Frenkel, Edward V.
1990
$${\mathcal W}_{1+\infty}$$ and $${\mathcal W}(gl_ N)$$ with central charge $$N$$. Zbl 0838.17028
Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang
1995
Langlands correspondence for loop groups. Zbl 1133.22009
Frenkel, Edward
2007
Wakimoto modules, opers and the center at the critical level. Zbl 1129.17014
Frenkel, Edward
2005
Quantum affine algebras and deformations of the Virasoro and $${\mathcal W}$$-algebras. Zbl 0869.17014
Frenkel, Edward; Reshetikhin, Nikolai
1996
Quantum $${\mathcal W}$$-algebras and elliptic algebras. Zbl 0871.17007
Feigin, Boris; Frenkel, Edward
1996
Representations of affine Kac-Moody algebras, bosonization and resolutions. Zbl 0711.17012
Feigin, Boris L.; Frenkel, Edward V.
1990
Baxter’s relations and spectra of quantum integrable models. Zbl 1332.82022
Frenkel, Edward; Hernandez, David
2015
Deformations of $$W$$-algebras associated to simple Lie algebras. Zbl 0939.17011
Frenkel, Edward; Reshetikhin, Nicolai
1998
Integrals of motion and quantum groups. Zbl 0885.58034
Feigin, Boris; Frenkel, Edward
1996
Local geometric Langlands correspondence and affine Kac-Moody algebras. Zbl 1184.17011
Frenkel, Edward; Gaitsgory, Dennis
2006
Gaudin models with irregular singularities. Zbl 1186.81065
Feigin, B.; Frenkel, E.; Toledano Laredo, V.
2010
Surface operators and separation of variables. Zbl 1388.81811
Frenkel, Edward; Gukov, Sergei; Teschner, Jörg
2016
Lectures on the Langlands program and conformal field theory. Zbl 1196.11091
Frenkel, Edward
2007
Semi-infinite Weil complex and the Virasoro algebra. Zbl 0726.17035
Feigin, Boris; Frenkel, Edward
1991
Quantization of soliton systems and Langlands duality. Zbl 1245.81062
Feigin, Boris; Frenkel, Edward
2011
A family of representations of affine Lie algebras. Zbl 0668.17015
Feigin, B. L.; Frenkel’, Edward V.
1988
The Hopf algebra $$\text{Rep\,} U_q \widehat{\mathfrak g\mathfrak l}_\infty$$. Zbl 1034.17009
Frenkel, E.; Mukhin, E.
2002
Quantum $$q$$-Langlands correspondence. Zbl 1422.22021
Aganagic, M.; Frenkel, E.; Okounkov, A.
2018
Affine algebras, Langlands duality and Bethe ansatz. Zbl 1052.17504
Frenkel, Edward
1995
Drinfeld-Sokolov reduction for difference operators and deformations of $${\mathcal W}$$-algebras. I: The case of Virasoro algebra. Zbl 0916.17020
Frenkel, E.; Reshetikhin, N.; Semenov-Tian-Shansky, M. A.
1998
Deformations of the KdV hierarchy and related soliton equations. Zbl 0860.17033
Frenkel, Edward
1996
Whittaker patterns in the geometry of moduli spaces of bundles on curves. Zbl 1070.11050
Frenkel, E.; Gaitsgory, D.; Vilonen, K.
2001
Instantons beyond topological theory. I. Zbl 1230.81050
Frenkel, E.; Losev, A.; Nekrasov, N.
2011
Opers with irregular singularity and spectra of the shift of argument subalgebra. Zbl 1226.22017
Feigin, Boris; Frenkel, Edward; Rybnikov, Leonid
2010
Geometric endoscopy and mirror symmetry. Zbl 1223.14014
Frenkel, Edward; Witten, Edward
2008
On the geometric Langlands conjecture. Zbl 1071.11039
Frenkel, E.; Gaitsgory, D.; Vilonen, K.
2002
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities. Zbl 0831.17012
Feigin, Boris; Frenkel, Edward
1993
Gaudin model and opers. Zbl 1132.17305
Frenkel, Edward
2005
Soliton equations, vertex operators, and simple singularities. Zbl 1203.37108
Frenkel, Edward; Givental, Alexander; Milanov, Todor
2010
A rigid irregular connection on the projective line. Zbl 1209.14017
Frenkel, Edward; Gross, Benedict
2009
A family of representations of affine Lie algebras. Zbl 0657.17013
Feĭgin, B. L.; Frenkel, Edward V.
1988
Trace formula and functionality: the beginnings of a program. (Formule des traces et fonctorialité: le début d’un programme.) Zbl 1267.11113
Frenkel, Edward; Langlands, Robert; Ngô, Bao Châu
2010
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers. Zbl 1397.81060
Frenkel, Edward; Hernandez, David
2018
Opers on the projective line, flag manifolds and Bethe Ansatz. Zbl 1087.82008
Frenkel, Edward
2004
$$D$$-modules on the affine Grassmannian and representations of affine Kac-Moody algebras. Zbl 1107.17013
Frenkel, Edward; Gaitsgory, Dennis
2004
Free field realizations in representation theory and conformal field theory. Zbl 0852.17023
Frenkel, Edward
1995
Thermodynamic Bethe ansatz and dilogarithm identities. I. Zbl 1036.11514
Frenkel, Edward; Szenes, András
1995
Duality in $$W$$-algebras. Zbl 0790.17013
Feigin, Boris; Frenkel, Edward
1991
Twisted modules over vertex algebras on algebraic curves. Zbl 1049.17024
Frenkel, Edward; Szczesny, Matthew
2004
Geometric realization of the Segal-Sugawara construction. Zbl 1170.17303
Ben-Zvi, David; Frenkel, Edward
2004
Spectral curves, opers and integrable systems. Zbl 1113.14301
Ben-Zvi, David; Frenkel, Edward
2001
D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Zbl 1251.17012
Frenkel, Edward; Gaitsgory, Dennis
2009
Geometric realization of Whittaker functions and the Langlands conjecture. Zbl 1068.11501
Frenkel, E.; Gaitsgory, D.; Kazhdan, D.; Vilonen, K.
1998
Integrable hierarchies and Wakimoto modules. Zbl 0977.17020
Feigin, Boris; Frenkel, Edward
1999
Mirror symmetry in two steps: A–I–B. Zbl 1127.14035
Frenkel, Edward; Losev, Andrei
2007
Localization of $$\mathfrak g$$-modules on the affine Grassmannian. Zbl 1202.17009
Frenkel, Edward; Gaitsgory, Dennis
2009
The $$q$$-characters at roots of unity. Zbl 1020.17009
Frenkel, Edward; Mukhin, Evgeny
2002
Bosonic ghost system and the Virasoro algebra. Zbl 1243.81086
Feigin, Boris; Frenkel, Edward
1990
Langlands duality for finite-dimensional representations of quantum affine algebras. Zbl 1222.17014
Frenkel, Edward; Hernandez, David
2011
Cohomology of the commutator subgroup of the braid group. Zbl 0675.20042
Frenkel’, Edward V.
1988
Quantum Langlands dualities of boundary conditions, $$D$$-modules, and conformal blocks. Zbl 1445.14024
Frenkel, Edward; Gaiotto, Davide
2020
Recent advances in the Langlands Program. Zbl 1070.11051
Frenkel, Edward
2004
Local geometric Langlands correspondence: the spherical case. Zbl 1192.17012
Frenkel, Edward; Gaitsgory, Dennis
2009
Geometric realizations of Wakimoto modules at the critical level. Zbl 1215.17016
Frenkel, Edward; Gaitsgory, Dennis
2008
Kac-Moody groups and integrability of soliton equations. Zbl 0829.58021
Feigin, Boris; Frenkel, Edward
1995
$$\mathcal W$$-algebras and Langlands-Drinfel’d correspondence. Zbl 1221.17023
Frenkel, Edward
1992
Gauge theory and Langlands duality. Zbl 1209.22009
Frenkel, Edward
2010
Fusion and convolution: applications to affine Kac-Moody algebras at the critical level. Zbl 1146.17025
Frenkel, Edward; Gaitsgory, Dennis
2006
Vertex algebras and algebraic curves. Zbl 0997.17015
Frenkel, Edward
2002
Representations of affine Kac-Moody algebras and bosonization. Zbl 0734.17011
Feĭgin, Boris L.; Frenkel, Edward V.
1990
Gerbal representations of double loop groups. Zbl 1280.22024
Frenkel, Edward; Zhu, Xinwen
2012
Geometrization of trace formulas. Zbl 1319.22015
Frenkel, Edward; Ngô, Bao Châu
2011
Langlands duality for representations of quantum groups. Zbl 1219.17007
Frenkel, Edward; Hernandez, David
2011
Weyl modules and opers without monodromy. Zbl 1231.17007
Frenkel, Edward; Gaitsgory, Dennis
2010
Equivalence of two approaches to integrable hierarchies of KdV type. Zbl 0873.35080
Enriquez, Benjamin; Frenkel, Edward
1997
Gromov-Witten gauge theory. Zbl 1342.14111
Frenkel, Edward; Teleman, Constantin; Tolland, A. J.
2016
Quantum Langlands duality of representations of $$\mathcal{W}$$-algebras. Zbl 07118442
Arakawa, Tomoyuki; Frenkel, Edward
2019
Love and math. The heart of hidden reality. Zbl 1319.00005
Frenkel, Edward
2013
Self-extensions of Verma modules and differential forms on opers. Zbl 1162.17314
Frenkel, Edward; Teleman, Constantin
2006
Chiral de Rham complex and orbifolds. Zbl 1184.14033
Frenkel, Edward; Szczesny, Matthew
2007
Ramification of the geometric Langlands program. Zbl 1194.22022
Frenkel, Edward
2008
Geometric interpretation of the Poisson structure in affine Toda field theories. Zbl 1047.37506
Enriquez, Benjamin; Frenkel, Edward
1998
Any flat bundle on a punctured disc has an oper structure. Zbl 1220.14013
Frenkel, Edward; Zhu, Xinwen
2010
Dilogarithm identities, $$q$$-difference equations, and the Virasoro algebra. Zbl 0783.17012
Frenkel, Edward; Szenes, Andras
1993
On strictly sparse subsets of a free group. Zbl 1126.20301
Averina, Ya. S.; Frenkel’, E. V.
2005
Erratum: Semi-infinite Weil complex and the Virasoro algebra. Zbl 0753.17033
Feigin, Boris; Frenkel, Edward
1992
Crystal bases, dilogarithm identities, and torsion in algebraic $$K$$-theory. Zbl 0848.17019
Frenkel, Edward; Szenes, András
1995
Five lectures on soliton equations. Zbl 0931.35147
Frenkel, Edward
1998
Langlands program, trace formulas, and their geometrization. Zbl 1329.11121
Frenkel, Edward
2013
An analytic version of the Langlands correspondence for complex curves. Zbl 07377937
Etingof, Pavel; Frenkel, Edward; Kazhdan, David
2021
Love and math. The heart of hidden reality. Translated from the English by Thomas Filk. Original English edition published by Basic Books, New York, NY, USA, 2013. (Liebe und Mathematik. Im Herzen einer verborgenen Wirklichkeit.) Zbl 1329.00026
Frenkel, Edward
2014
Amalgamated products of groups: measures of random normal forms. Zbl 1259.20032
Myasnikov, A. G.; Remeslennikov, V. N.; Frenkel, E. V.
2012
An analytic version of the Langlands correspondence for complex curves. Zbl 07377937
Etingof, Pavel; Frenkel, Edward; Kazhdan, David
2021
Quantum Langlands dualities of boundary conditions, $$D$$-modules, and conformal blocks. Zbl 1445.14024
Frenkel, Edward; Gaiotto, Davide
2020
Quantum Langlands duality of representations of $$\mathcal{W}$$-algebras. Zbl 07118442
Arakawa, Tomoyuki; Frenkel, Edward
2019
Quantum $$q$$-Langlands correspondence. Zbl 1422.22021
Aganagic, M.; Frenkel, E.; Okounkov, A.
2018
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers. Zbl 1397.81060
Frenkel, Edward; Hernandez, David
2018
Surface operators and separation of variables. Zbl 1388.81811
Frenkel, Edward; Gukov, Sergei; Teschner, Jörg
2016
Gromov-Witten gauge theory. Zbl 1342.14111
Frenkel, Edward; Teleman, Constantin; Tolland, A. J.
2016
Baxter’s relations and spectra of quantum integrable models. Zbl 1332.82022
Frenkel, Edward; Hernandez, David
2015
Love and math. The heart of hidden reality. Translated from the English by Thomas Filk. Original English edition published by Basic Books, New York, NY, USA, 2013. (Liebe und Mathematik. Im Herzen einer verborgenen Wirklichkeit.) Zbl 1329.00026
Frenkel, Edward
2014
Love and math. The heart of hidden reality. Zbl 1319.00005
Frenkel, Edward
2013
Langlands program, trace formulas, and their geometrization. Zbl 1329.11121
Frenkel, Edward
2013
Gerbal representations of double loop groups. Zbl 1280.22024
Frenkel, Edward; Zhu, Xinwen
2012
Amalgamated products of groups: measures of random normal forms. Zbl 1259.20032
Myasnikov, A. G.; Remeslennikov, V. N.; Frenkel, E. V.
2012
Quantization of soliton systems and Langlands duality. Zbl 1245.81062
Feigin, Boris; Frenkel, Edward
2011
Instantons beyond topological theory. I. Zbl 1230.81050
Frenkel, E.; Losev, A.; Nekrasov, N.
2011
Langlands duality for finite-dimensional representations of quantum affine algebras. Zbl 1222.17014
Frenkel, Edward; Hernandez, David
2011
Geometrization of trace formulas. Zbl 1319.22015
Frenkel, Edward; Ngô, Bao Châu
2011
Langlands duality for representations of quantum groups. Zbl 1219.17007
Frenkel, Edward; Hernandez, David
2011
Gaudin models with irregular singularities. Zbl 1186.81065
Feigin, B.; Frenkel, E.; Toledano Laredo, V.
2010
Opers with irregular singularity and spectra of the shift of argument subalgebra. Zbl 1226.22017
Feigin, Boris; Frenkel, Edward; Rybnikov, Leonid
2010
Soliton equations, vertex operators, and simple singularities. Zbl 1203.37108
Frenkel, Edward; Givental, Alexander; Milanov, Todor
2010
Trace formula and functionality: the beginnings of a program. (Formule des traces et fonctorialité: le début d’un programme.) Zbl 1267.11113
Frenkel, Edward; Langlands, Robert; Ngô, Bao Châu
2010
Gauge theory and Langlands duality. Zbl 1209.22009
Frenkel, Edward
2010
Weyl modules and opers without monodromy. Zbl 1231.17007
Frenkel, Edward; Gaitsgory, Dennis
2010
Any flat bundle on a punctured disc has an oper structure. Zbl 1220.14013
Frenkel, Edward; Zhu, Xinwen
2010
A rigid irregular connection on the projective line. Zbl 1209.14017
Frenkel, Edward; Gross, Benedict
2009
D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Zbl 1251.17012
Frenkel, Edward; Gaitsgory, Dennis
2009
Localization of $$\mathfrak g$$-modules on the affine Grassmannian. Zbl 1202.17009
Frenkel, Edward; Gaitsgory, Dennis
2009
Local geometric Langlands correspondence: the spherical case. Zbl 1192.17012
Frenkel, Edward; Gaitsgory, Dennis
2009
Geometric endoscopy and mirror symmetry. Zbl 1223.14014
Frenkel, Edward; Witten, Edward
2008
Geometric realizations of Wakimoto modules at the critical level. Zbl 1215.17016
Frenkel, Edward; Gaitsgory, Dennis
2008
Ramification of the geometric Langlands program. Zbl 1194.22022
Frenkel, Edward
2008
Langlands correspondence for loop groups. Zbl 1133.22009
Frenkel, Edward
2007
Lectures on the Langlands program and conformal field theory. Zbl 1196.11091
Frenkel, Edward
2007
Mirror symmetry in two steps: A–I–B. Zbl 1127.14035
Frenkel, Edward; Losev, Andrei
2007
Chiral de Rham complex and orbifolds. Zbl 1184.14033
Frenkel, Edward; Szczesny, Matthew
2007
Local geometric Langlands correspondence and affine Kac-Moody algebras. Zbl 1184.17011
Frenkel, Edward; Gaitsgory, Dennis
2006
Fusion and convolution: applications to affine Kac-Moody algebras at the critical level. Zbl 1146.17025
Frenkel, Edward; Gaitsgory, Dennis
2006
Self-extensions of Verma modules and differential forms on opers. Zbl 1162.17314
Frenkel, Edward; Teleman, Constantin
2006
Wakimoto modules, opers and the center at the critical level. Zbl 1129.17014
Frenkel, Edward
2005
Gaudin model and opers. Zbl 1132.17305
Frenkel, Edward
2005
On strictly sparse subsets of a free group. Zbl 1126.20301
Averina, Ya. S.; Frenkel&rsquo;, E. V.
2005
Vertex algebras and algebraic curves. 2nd revised and expanded ed. Zbl 1106.17035
Frenkel, Edward; Ben-Zvi, David
2004
Opers on the projective line, flag manifolds and Bethe Ansatz. Zbl 1087.82008
Frenkel, Edward
2004
$$D$$-modules on the affine Grassmannian and representations of affine Kac-Moody algebras. Zbl 1107.17013
Frenkel, Edward; Gaitsgory, Dennis
2004
Twisted modules over vertex algebras on algebraic curves. Zbl 1049.17024
Frenkel, Edward; Szczesny, Matthew
2004
Geometric realization of the Segal-Sugawara construction. Zbl 1170.17303
Ben-Zvi, David; Frenkel, Edward
2004
Recent advances in the Langlands Program. Zbl 1070.11051
Frenkel, Edward
2004
The Hopf algebra $$\text{Rep\,} U_q \widehat{\mathfrak g\mathfrak l}_\infty$$. Zbl 1034.17009
Frenkel, E.; Mukhin, E.
2002
On the geometric Langlands conjecture. Zbl 1071.11039
Frenkel, E.; Gaitsgory, D.; Vilonen, K.
2002
The $$q$$-characters at roots of unity. Zbl 1020.17009
Frenkel, Edward; Mukhin, Evgeny
2002
Vertex algebras and algebraic curves. Zbl 0997.17015
Frenkel, Edward
2002
Vertex algebras and algebraic curves. Zbl 0981.17022
Frenkel, Edward; Ben-Zvi, David
2001
Combinatorics of $$q$$-characters of finite-dimensional representations of quantum affine algebras. Zbl 1051.17013
Frenkel, Edward; Mukhin, Evgeny
2001
Whittaker patterns in the geometry of moduli spaces of bundles on curves. Zbl 1070.11050
Frenkel, E.; Gaitsgory, D.; Vilonen, K.
2001
Spectral curves, opers and integrable systems. Zbl 1113.14301
Ben-Zvi, David; Frenkel, Edward
2001
The $$q$$-characters of representations of quantum affine algebras and deformations of $$W$$-algebras. Zbl 0973.17015
Frenkel, Edward; Reshetikhin, Nicolai
1999
Integrable hierarchies and Wakimoto modules. Zbl 0977.17020
Feigin, Boris; Frenkel, Edward
1999
Deformations of $$W$$-algebras associated to simple Lie algebras. Zbl 0939.17011
Frenkel, Edward; Reshetikhin, Nicolai
1998
Drinfeld-Sokolov reduction for difference operators and deformations of $${\mathcal W}$$-algebras. I: The case of Virasoro algebra. Zbl 0916.17020
Frenkel, E.; Reshetikhin, N.; Semenov-Tian-Shansky, M. A.
1998
Geometric realization of Whittaker functions and the Langlands conjecture. Zbl 1068.11501
Frenkel, E.; Gaitsgory, D.; Kazhdan, D.; Vilonen, K.
1998
Geometric interpretation of the Poisson structure in affine Toda field theories. Zbl 1047.37506
Enriquez, Benjamin; Frenkel, Edward
1998
Five lectures on soliton equations. Zbl 0931.35147
Frenkel, Edward
1998
Equivalence of two approaches to integrable hierarchies of KdV type. Zbl 0873.35080
Enriquez, Benjamin; Frenkel, Edward
1997
Quantum affine algebras and deformations of the Virasoro and $${\mathcal W}$$-algebras. Zbl 0869.17014
Frenkel, Edward; Reshetikhin, Nikolai
1996
Quantum $${\mathcal W}$$-algebras and elliptic algebras. Zbl 0871.17007
Feigin, Boris; Frenkel, Edward
1996
Integrals of motion and quantum groups. Zbl 0885.58034
Feigin, Boris; Frenkel, Edward
1996
Deformations of the KdV hierarchy and related soliton equations. Zbl 0860.17033
Frenkel, Edward
1996
$${\mathcal W}_{1+\infty}$$ and $${\mathcal W}(gl_ N)$$ with central charge $$N$$. Zbl 0838.17028
Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang
1995
Affine algebras, Langlands duality and Bethe ansatz. Zbl 1052.17504
Frenkel, Edward
1995
Free field realizations in representation theory and conformal field theory. Zbl 0852.17023
Frenkel, Edward
1995
Thermodynamic Bethe ansatz and dilogarithm identities. I. Zbl 1036.11514
Frenkel, Edward; Szenes, András
1995
Kac-Moody groups and integrability of soliton equations. Zbl 0829.58021
Feigin, Boris; Frenkel, Edward
1995
Crystal bases, dilogarithm identities, and torsion in algebraic $$K$$-theory. Zbl 0848.17019
Frenkel, Edward; Szenes, András
1995
Gaudin model, Bethe ansatz and critical level. Zbl 0812.35103
Feigin, Boris; Frenkel, Edward; Reshetikhin, Nikolai
1994
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities. Zbl 0831.17012
Feigin, Boris; Frenkel, Edward
1993
Dilogarithm identities, $$q$$-difference equations, and the Virasoro algebra. Zbl 0783.17012
Frenkel, Edward; Szenes, Andras
1993
Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras. Zbl 0925.17022
Feigin, Boris; Frenkel, Edward
1992
Characters and fusion rules for $$W$$-algebras via quantized Drinfeld- Sokolov reduction. Zbl 0768.17008
Frenkel, Edward; Kac, Victor; Wakimoto, Minoru
1992
$$\mathcal W$$-algebras and Langlands-Drinfel’d correspondence. Zbl 1221.17023
Frenkel, Edward
1992
Erratum: Semi-infinite Weil complex and the Virasoro algebra. Zbl 0753.17033
Feigin, Boris; Frenkel, Edward
1992
Semi-infinite Weil complex and the Virasoro algebra. Zbl 0726.17035
Feigin, Boris; Frenkel, Edward
1991
Duality in $$W$$-algebras. Zbl 0790.17013
Feigin, Boris; Frenkel, Edward
1991
Quantization of the Drinfel’d-Sokolov reduction. Zbl 1242.17023
Feigin, Boris; Frenkel, Edward
1990
Affine Kac-Moody algebras and semi-infinite flag manifolds. Zbl 0722.17019
Feigin, Boris L.; Frenkel, Edward V.
1990
Representations of affine Kac-Moody algebras, bosonization and resolutions. Zbl 0711.17012
Feigin, Boris L.; Frenkel, Edward V.
1990
Bosonic ghost system and the Virasoro algebra. Zbl 1243.81086
Feigin, Boris; Frenkel, Edward
1990
Representations of affine Kac-Moody algebras and bosonization. Zbl 0734.17011
Feĭgin, Boris L.; Frenkel, Edward V.
1990
A family of representations of affine Lie algebras. Zbl 0668.17015
Feigin, B. L.; Frenkel&rsquo;, Edward V.
1988
A family of representations of affine Lie algebras. Zbl 0657.17013
Feĭgin, B. L.; Frenkel, Edward V.
1988
Cohomology of the commutator subgroup of the braid group. Zbl 0675.20042
Frenkel&rsquo;, Edward V.
1988
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#### Cited by 1,079 Authors

 37 Feĭgin, Boris L’vovich 36 Frenkel, Edward V. 28 Arakawa, Tomoyuki 28 Mukhin, Evgeny 26 Linshaw, Andrew Ross 25 Creutzig, Thomas 18 Adamović, Dražen 18 Kac, Victor G. 18 Molev, Alexander I. 15 Hernandez, David 14 Futorny, Vyacheslav M. 13 Cox, Ben Lewis 12 Li, Haisheng 11 Gaitsgory, Dennis 11 Jimbo, Michio 11 Jing, Naihuan 11 Milas, Antun 11 Oh, Se-jin 11 Ragoucy, Eric 11 Varchenko, Alexander Nikolaevich 11 Young, Charles A. S. 10 Awata, Hidetoshi 10 Lukyanov, Sergei L. 10 Vicedo, Benoît 10 Zeitlin, Anton M. 9 Bakalov, Bojko 9 Kimura, Taro 9 Ridout, David 9 Shiraishi, Jun’ichi 9 Zabzine, Maxim 8 Feigin, Evgeny 8 Heluani, Reimundo 8 Nekrasov, Nikita Alexandrovich 8 Rybnikov, Leonid Grigor’evich 8 Wakimoto, Minoru 7 Bazhanov, Vladimir V. 7 Chari, Vyjayanthi 7 De Sole, Alberto 7 Ding, Xiangmao 7 Duncan, John F. R. 7 Frenkel, Igor B. 7 Gukov, Sergei 7 Kedem, Rinat 7 Malikov, Fyodor 7 Manojlović, Nenad 7 Miwa, Tetsuji 7 Nakanishi, Tomoki 7 Odake, Satoru 7 Tsuboi, Zengo 6 António, N. Cirilo 6 Bershteĭn, Mikhaĭl Aleksandrovich 6 Bezrukavnikov, Roman 6 Di Francesco, Philippe 6 Etingof, Pavel Il’ich 6 Falqui, Gregorio 6 Fuchs, Jürgen 6 Genra, Naoki 6 Hou, Boyu 6 Kanade, Shashank 6 Kojima, Takeo 6 Liu, Siqi 6 Moreau, Anne 6 Morozov, Alexei Yurievich 6 Moura, Adriano A. 6 Pestun, Vasily 6 Razumov, Alexander V. 6 Runkel, Ingo 6 Semikhatov, Alexei M. 6 Wang, Weiqiang 6 Zenkevich, Yegor 6 Zhang, Huafeng 6 Zhang, Youjin 5 Anguelova, Iana I. 5 Biswas, Indranil 5 Bourgine, Jean-Emile 5 Callegaro, Filippo 5 Dubrovin, Boris Anatol’evich 5 Enriquez, Benjamin 5 Frappat, Luc 5 Gaiotto, Davide 5 Jiang, Cuipo 5 Kashiwara, Masaki 5 Koshida, Shinji 5 Kuniba, Atsuo 5 Li, Jian Rong 5 Masoero, Davide 5 Mironov, Andrei D. 5 Nieri, Fabrizio 5 Pei, Yufeng 5 Plaza Martín, Francisco José 5 Su, Yucai 5 Suh, Uhi Rinn 5 Szczesny, Matthew 5 Teschner, Jörg 5 Valeri, Daniele 5 van Ekeren, Jethro 5 Vasserot, Eric 5 Yakimova, Oksana S. 5 Yanagida, Shintarou 5 Yang, Jinwei ...and 979 more Authors
all top 5

#### Cited in 151 Serials

 147 Communications in Mathematical Physics 101 Journal of High Energy Physics 79 Advances in Mathematics 69 Letters in Mathematical Physics 67 Nuclear Physics. B 63 Journal of Mathematical Physics 58 Journal of Algebra 32 Selecta Mathematica. New Series 27 Journal of Geometry and Physics 24 Theoretical and Mathematical Physics 24 Duke Mathematical Journal 23 Transactions of the American Mathematical Society 19 Transformation Groups 16 Representation Theory 14 Compositio Mathematica 14 Communications in Contemporary Mathematics 13 Mathematische Zeitschrift 12 Inventiones Mathematicae 12 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 11 Journal of Pure and Applied Algebra 11 Algebras and Representation Theory 10 Bulletin of the American Mathematical Society. New Series 10 Annals of Mathematics. Second Series 9 International Journal of Modern Physics A 9 Journal of the American Mathematical Society 9 Science China. Mathematics 8 Communications in Algebra 8 Proceedings of the American Mathematical Society 8 Journal of the Institute of Mathematics of Jussieu 7 Functional Analysis and its Applications 7 Journal of Nonlinear Mathematical Physics 6 Mathematische Annalen 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 International Journal of Mathematics 6 Journal of the European Mathematical Society (JEMS) 6 Japanese Journal of Mathematics. 3rd Series 5 Israel Journal of Mathematics 5 Reviews in Mathematical Physics 5 Annales de l’Institut Fourier 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Journal of Algebraic Geometry 5 Journal of Algebra and its Applications 5 Journal of Physics A: Mathematical and Theoretical 4 International Journal of Modern Physics B 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Transactions of the Moscow Mathematical Society 4 Journal of Algebraic Combinatorics 4 The Ramanujan Journal 3 Modern Physics Letters A 3 Applied Mathematics and Computation 3 Publications Mathématiques 3 Journal of Functional Analysis 3 Journal für die Reine und Angewandte Mathematik 3 Memoirs of the American Mathematical Society 3 Nagoya Mathematical Journal 3 Chinese Annals of Mathematics. Series B 3 Acta Applicandae Mathematicae 3 Annales Henri Poincaré 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Central European Journal of Mathematics 3 Journal of Statistical Mechanics: Theory and Experiment 3 Advances in Mathematical Physics 3 Kyoto Journal of Mathematics 3 European Journal of Mathematics 2 Reports on Mathematical Physics 2 Journal of the Mathematical Society of Japan 2 Journal of Number Theory 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the London Mathematical Society. Third Series 2 Journal of Knot Theory and its Ramifications 2 Algebra Colloquium 2 Journal of Mathematical Sciences (New York) 2 Séminaire Lotharingien de Combinatoire 2 Foundations of Science 2 Czechoslovak Journal of Physics 2 Algebraic & Geometric Topology 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Frontiers of Mathematics in China 2 Journal of Noncommutative Geometry 2 Algebra & Number Theory 2 Communications in Theoretical Physics 2 Forum of Mathematics, Sigma 2 Annales Mathématiques du Québec 2 Research in the Mathematical Sciences 2 Journal de l’École Polytechnique – Mathématiques 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematische Semesterberichte 1 Physics Letters. B 1 Russian Mathematical Surveys 1 Chaos, Solitons and Fractals 1 The Mathematical Intelligencer 1 Acta Mathematica Vietnamica 1 Geometriae Dedicata 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Mathematische Nachrichten ...and 51 more Serials
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#### Cited in 47 Fields

 687 Nonassociative rings and algebras (17-XX) 563 Quantum theory (81-XX) 232 Algebraic geometry (14-XX) 106 Dynamical systems and ergodic theory (37-XX) 95 Statistical mechanics, structure of matter (82-XX) 89 Group theory and generalizations (20-XX) 84 Number theory (11-XX) 80 Associative rings and algebras (16-XX) 78 Topological groups, Lie groups (22-XX) 58 Category theory; homological algebra (18-XX) 49 Differential geometry (53-XX) 46 Partial differential equations (35-XX) 45 Relativity and gravitational theory (83-XX) 41 Combinatorics (05-XX) 41 Global analysis, analysis on manifolds (58-XX) 39 Commutative algebra (13-XX) 39 Special functions (33-XX) 29 Several complex variables and analytic spaces (32-XX) 26 Manifolds and cell complexes (57-XX) 18 $$K$$-theory (19-XX) 16 Ordinary differential equations (34-XX) 14 Mechanics of particles and systems (70-XX) 13 Functional analysis (46-XX) 12 Functions of a complex variable (30-XX) 11 Probability theory and stochastic processes (60-XX) 9 Difference and functional equations (39-XX) 8 Algebraic topology (55-XX) 7 General and overarching topics; collections (00-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Statistics (62-XX) 4 History and biography (01-XX) 4 Field theory and polynomials (12-XX) 4 Abstract harmonic analysis (43-XX) 4 Operator theory (47-XX) 4 Geometry (51-XX) 3 Numerical analysis (65-XX) 3 Computer science (68-XX) 2 Potential theory (31-XX) 2 Convex and discrete geometry (52-XX) 2 Fluid mechanics (76-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

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