Boris Feigin

Gaudin model, Bethe Ansatz and critical level

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.

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

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.

Quantization of the Drinfeld-Sokolov reduction

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.

Quantum

AbstractWe define a quantum-algebra associated to

-algebras and elliptic algebras

\mathfrak{s}\mathfrak{l}_N

Super Liouville conformal blocks from N = 2 SU(2) quiver gauge theories

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

Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models.

\mathfrak{s}\mathfrak{l}_N