Representations of Degenerate Affine Hecke Algebra of Type $C_n$ Under the Etingof-Freund-Ma Functor

TL;DR

This paper computes the image of polynomial $GL_N$-modules under the Etingof-Freund-Ma functor for the degenerate affine Hecke algebra of type $C_n$, providing a combinatorial description and analyzing weights.

Contribution

It offers a new combinatorial framework for understanding the functor's image on polynomial modules of $GL_N$ in the context of type $C_n$ affine Hecke algebras.

Findings

Explicit combinatorial description using standard tableaux

Analysis of weights via contents of tableaux

Application to representations of degenerate affine Hecke algebra of type $C_n$

Abstract

We compute the image of a polynomial $GL_N$-module under the Etingof-Freund-Ma functor \cite{EFM}. We give a combinatorial description of the image in terms of standard tableaux on a collection of skew shapes and analyze weights of the image in terms of contents.