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Dive into the research topics where Edward Frenkel is active.

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Featured researches published by Edward Frenkel.


Communications in Mathematical Physics | 1994

Gaudin model, Bethe Ansatz and critical level

Boris Feigin; Edward Frenkel; Nikolai Reshetikhin

We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these hamiltonians by restricting certain invariant functionals on tensoproducts of Wakimoto modules. This gives explicit formulas for the eigenvectors via bosonic correlation functions. Analogues of the Bethe Ansatz equations naturally appear as equations on the existence of singular vectors in Wakimoto modules. We use this construction to explain the connection between Gaudins model and correlation functios of WZNW models.


International Journal of Modern Physics A | 1992

AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS

Boris Feigin; Edward Frenkel

We prove Drinfelds conjecture that the center of a certain completion of the universal enveloping algebra of an affine Kac-Moody algebra at the critical level is isomorphic to the Gelfand-Dikii algebra, associated to the Langlands dual algebra. The center is identified with a limit of the W-algebra, defined by means of the quantum Drinfeld-Sokolov reduction.


Physics Letters B | 1990

Quantization of the Drinfeld-Sokolov reduction

Boris Feigin; Edward Frenkel

Abstract We show that the quantum Drinfeld-Sokolov reduction of the affine Kac-Moody algebra sl( n ) Λ gives the W n -algebra of Fateev-Zamolodchikov-Lukyanov. We derive this W n -algebra explicitly as a BRST cohomology algebra, using the homological technique of spectral sequences.


Communications in Mathematical Physics | 1990

Affine Kac-Moody algebras and semi-infinite flag manifolds

Boris L. Geigin; Edward Frenkel

We study representations of affine Kac-Moody algebras from a geometric point of view. It is shown that Wakimoto modules introduced in [18], which are important in conformal field theory, correspond to certain sheaves on a semi-infinite flag manifold with support on its Schhubert cells. This manifold is equipped with a remarkable semi-infinite structure, which is discussed; in particular, the semi-infinite homology of this manifold is computed. The Cousin-Grothendieck resolution of an invertible sheaf on a semi-infinite flag manifold gives a two-sided resolution of an irreducible representation of an affine algebras, consisting of Wakimoto modules. This is just the BRST complex. As a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent Lie algebra.


Communications in Mathematical Physics | 1992

Characters and fusion rules for

Edward Frenkel; Victor G. Kac; Minoru Wakimoto

Using the cohomological approach toW-algebras, we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the quantized Drinfeld-Sokolov reduction.


Communications in Mathematical Physics | 1996

W

Boris Feigin; Edward Frenkel

AbstractWe define a quantum-algebra associated to


arXiv: High Energy Physics - Theory | 2005

-algebras via quantized Drinfel'd-Sokolov reduction

Edward Frenkel


Communications in Mathematical Physics | 1996

Quantum

Edward Frenkel; Nikolai Reshetikhin

\mathfrak{s}\mathfrak{l}_N


Communications in Mathematical Physics | 2001

\scr W

Edward Frenkel; Evgeny Mukhin


Archive | 2014

-algebras and elliptic algebras

Edward Frenkel

as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of

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David Ben-Zvi

University of Texas at Austin

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Victor G. Kac

Massachusetts Institute of Technology

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Andrey Radul

Massachusetts Institute of Technology

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David Hernandez

École Normale Supérieure

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