Lie algebras and degenerate Affine Hecke Algebras of type A

TL;DR

This paper constructs exact functors linking Lie algebra representations to degenerate affine Hecke algebra modules, enabling the classification of all simple modules in the latter category.

Contribution

It introduces a new family of exact functors from the BGG category of sl to finite-dimensional H-modules, connecting two important representation theories.

Findings

Functors transform Verma modules to standard modules or zero.

Simple modules in H can be obtained via these functors.

All simple H-modules are accessible through this construction.

Abstract

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple H-module can be thus obtained.