Representations of Infinite-dimensional Lie Algebras

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