### View Abstract

Abstract: The category of Whittaker modules is a category of Lie algebra

representations which generalizes other well-studied categories of

representations, such as the Bernstein-Gelfand-Gelfand category O. In this

talk we will construct a family of exact functors from the category of

Whittaker modules to the category of finite-dimensional graded affine

Hecke algebra modules, for type A_n. These algebraically defined functors

provide us with a representation theoretic analogue of certain geometric

relationships, observed independently by Zelevinsky and Lusztig, between

the flag variety and the variety of graded nilpotent classes. Using this

geometric perspective and the corresponding Kazhdan-Lusztig conjectures

for each category, we will prove that these functors map simple modules to

simple modules (or zero). Moreover, we will see that each simple module

for the graded affine Hecke algebra can be realized as the image of a

simple Whittaker module.