Representations of Infinite-dimensional Lie Algebras

Indiana University, Bloomington IN

Investigators

Abstract

Abstract Mukhin E. Mukhin studies the representation theory of affine Lie algebras and their quantizations in several directions including the theory of coinvariants of integrable representations of affine Kac-Moody algebras (with B. Feigin, M. Jimbo and T. Miwa), the theory of finite-dimensional representations of quantum affine groups (with E. Frenkel) and the functors between categories of representations of Lie algebras and quantum groups defined by Knizhnik-Zamolodchikov and quantized Knizhnik-Zamolodchikov equations (with A. Varchenko). The project is expected to result in description of many features of the beautiful algebraic-combinatorial structure related to representation theory of complex semi-simple Lie algebras and their affine and quantum analogs. In particular, this research has connections to many areas of mathematics such as theory of symmetric functions and combinatorics of Young tableaux, theory of special functions, exactly solvable lattice models, conformal field theory, massive field theory in 1+1 dimensions, etc; as all these theories have symmetries described in terms of Lie algebras of different kind.