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Geometric realizations of affine Kac-Moody algebras (1610.07973v1)
Published 25 Oct 2016 in math.RT, math-ph, math.AG, math.FA, math.MP, and math.OA
Abstract: The goal of the present paper is to obtain new free field realizations of affine Kac-Moody algebras motivated by geometric representation theory for generalized flag manifolds of finite-dimensional semisimple Lie groups. We provide an explicit construction of a large class of irreducible modules associated with certain parabolic subalgebras covering all known special cases.