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

TL;DR

This paper constructs a Yangian action on higher level irreducible modules of affine gl(N), linking it to degenerate double affine Hecke algebra representations and decomposing modules via semi-infinite skew Young diagrams.

Contribution

It introduces a novel Yangian action on affine gl(N) modules at levels greater than one, derived through Drinfeld duality and semi-infinite limits, and decomposes modules using intertwiners and skew Young diagrams.

Findings

Yangian action defined on affine gl(N) modules at level > 1

Modules decomposed into irreducible Yangian subrepresentations

Decomposition parameterized by semi-infinite skew Young diagrams

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.