Edward Frenkel
University of California
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Featured researches published by Edward Frenkel.
Communications in Mathematical Physics | 1994
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
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
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
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
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
Boris Feigin; Edward Frenkel
AbstractWe define a quantum-algebra associated to
arXiv: High Energy Physics - Theory | 2005
Edward Frenkel
Communications in Mathematical Physics | 1996
Edward Frenkel; Nikolai Reshetikhin
\mathfrak{s}\mathfrak{l}_N
Communications in Mathematical Physics | 2001
Edward Frenkel; Evgeny Mukhin
Archive | 2014
Edward Frenkel
as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of