Skew Schur Functions and Yangian Actions on Irreducible Integrable Modules of $ \hat{\frak g \frak l} _N $

Abstract

An action of the Yangian of the general linear Lie algebra \( {\frak g \frak l} _N \) is defined on every irreducible integrable highest weight module of \( \hat{\frak g \frak l} _N \). 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 \( \frak H \). Each vacuum module of \( \hat{\frak g \frak l} _N \) is decomposed into irreducible Yangian representations by means of the intertwiners of \( \frak H \). Components of this decomposition are parameterized by semi-infinite skew Young diagrams. The decomposition gives rise to a character formulas for the modules of \( \hat{\frak g \frak l} _N \) in terms of skew Schur functions.