Annals of Combinatorics 4 (2000) 383-400


Skew Schur Functions and Yangian Actions on Irreducible Integrable Modules of $ \widehat{{\mathfrak{gl}}}_N$

Denis Uglov

Research Institute for Mathematical Sciences, Kyoto University, 606 Kyoto, Japan
duglov@kurims.kyoto-u.ac.jp

Received March 26, 1999

AMS Subject Classification: 17B67, 17B37, 17B81

Abstract. An action of the Yangian of the general linear Lie algebra $ \mathfrak{gl}_N$ is defined on every irreducible integrable highest weight module of $ \widehat{{\mathfrak{gl}}}_N$. This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra$ \mathfrak{H}.$ Each vacuum modul e of $ \widehat{{\mathfrak{gl}}}_N$ is decomposed into irreducible Yangian representations by means of the intertwiners of $ \mathfrak{H}.$ Components of this decomposition are parameterized by semi-infinite skew Young diagrams. The decomposition gives rise to a character formulas for the modules of $ \widehat{{\mathfrak{gl}}}_N$ in terms of skew Schur functions.

Keywords: Representation of affine Lie algebra, Yangian action , skew Young diagram, skew schur functions


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