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- Publications
- Influence

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

- B. Feigin, E. Frenkel
- Physics
- 1 April 1992

We prove Drinfeld's 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… Expand

A commutative algebra on degenerate CP1 and Macdonald polynomials

- B. Feigin, K. Hashizume, A. Hoshino, J. Shiraishi, S. Yanagida
- Mathematics
- 15 April 2009

We introduce a unital associative algebra A associated with degenerate CP1. We show that A is a commutative algebra and whose Poincare series is given by the number of partitions. Thereby, we can… Expand

QuantumOpen image in new window-algebras and elliptic algebras

- B. Feigin, E. Frenkel
- Physics
- 1 July 1996

We define a quantum
Open image in new window
-algebra associated to\(\mathfrak{s}\mathfrak{l}_N \) as an associative algebra depending on two parameters. For special values of the parameters, this… Expand

Quantization of the Drinfeld-Sokolov reduction

- B. Feigin, E. Frenkel
- Physics
- 23 August 1990

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… Expand

Gaudin model, Bethe Ansatz and critical level

- B. Feigin, E. Frenkel, N. Reshetikhin
- Physics, Mathematics
- 3 February 1994

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… Expand

Super Liouville conformal blocks from $ \mathcal{N} = 2 $ SU(2) quiver gauge theories

- V. Belavin, B. Feigin
- Physics
- 29 May 2011

The conjecture about the correspondence between instanton partition functions in the N = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the… Expand

Quantum-algebras and elliptic algebras

- B. Feigin, E. Frenkel
- Mathematics, Physics
- 17 August 1995

AbstractWe define a quantum-algebra associated to
$$\mathfrak{s}\mathfrak{l}_N $$
as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes… Expand

Hochschild cohomology of the Weyl algebra and traces in deformation quantization

- B. Feigin, G. Felder, B. Shoikhet
- Mathematics
- 18 November 2003

We give a formula for a cocycle generating the Hochschild cohomology of the Weyl algebra with coefficients in its dual.It is given by an integral over the configuration space of ordered points on a… Expand

A differential ideal of symmetric polynomials spanned by Jack polynomials at rβ = -(r=1)/(k+1)

- B. Feigin, Michio Jimbo, T. Miwa, E. Mukhin
- Mathematics
- 12 December 2001

For each pair of positive integers (k,r) such that k+1,r-1 are coprime, we introduce an ideal $I^{(k,r)}_n$ of the ring of symmetric polynomials. The ideal $I^{(k,r)}_n$ has a basis consisting of… Expand