Classification of irreducible $\mathfrak{u}$-diagonalizable $H_{\ell,n}$-modules

TL;DR

This paper classifies irreducible modules of the degenerate affine Hecke algebra of type G(ell,1,n) that are diagonalizable, showing they correspond to skew shapes and have bases indexed by Young tableaux.

Contribution

It provides a complete classification of irreducible, diagonalizable modules of the algebra, linking them to combinatorial objects like skew shapes and Young tableaux.

Findings

Modules are indexed by ell-skew shapes.

Each module has a basis of eigenvectors labeled by standard Young tableaux.

Classification extends understanding of representation theory for this algebra.

Abstract

We give a classification for the irreducible $\mathfrak{u}$-diagonalizable representations of the degenerate affine Hecke algebra of type $G(\ell,1,n)$. Precisely we show that such $H_{\ell,n}$-modules are indexed by $\ell$-skew shapes and that the representation indexed by a skew shape $D$ has a basis of eigenvectors indexed by standard Young tableaux of shape $D$.