Representations of Degenerate Affine Hecke Algebra and $\mathfrak{g}\mathfrak{l}_{n}$

Abstract

We study the representation theory of the degenerate affine Hecke algebra $H_\ell$ of $GL_\ell$ using functors that connect the representation theory of $H_\ell$ and that of the Lie algebra $\mathfrak{gl}_n$. In particular, a new algebraic approach to the classification theorem of simple $H_\ell$-modules is given.