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

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 $D$.