Yangian actions on higher level irreducible integrable modules of affine gl(N)

Abstract

An action of the Yangian of the general Lie algebra gl(N) is defined on every irreducible integrable highest weight module of affine gl(N) with level greater than 1. This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra H. Each vacuum module of affine gl(N) is decomposed into irreducible Yangian subrepresentations by means of the intertwiners of H. Components of this decomposition are parameterized by semi-infinite skew Young diagrams.

arXiv commentLaTeX, 42 pages. A new section (3.2.2) is added. This section contains expressions for the generators of the sl(N)-Yangian action on an irreducible integrable module of gl(N)^ in terms of the standard generators of gl(N)^

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• An integrable $U_q(\widehat{gl}(2|2){)}_1$-Model: Corner Transfer Matrices and Young Skew Diagrams