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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.