Lie algebras and degenerate Affine Hecke Algebras of type A

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.

15 pages, AMS-LaTex, some typos are corrected; some minor changes are made. to appear in Journal of Algebra, with the title ``Duality between ${\mathfrak{sl}}_n(\mathbb{C})$ and the degenerate affine Hecke algebra''