Abstract from the Pacific Journal of Mathematics

Volume 180, Number 2, October 1997

Title: On Springer Representations and the Zuckerman Functor

Author: Sam Evens

Abstract:

The purpose of this note is to resolve some questions raised by Hunziker and Wallach. Wallach has given a beautiful, simple algebraic approach to the Springer representations. Hunziker and Wallach have given a conjectural reinterpretation of this result which depends on a computation of the Zuckerman functor. We do this calculation using the geometric interpretation of the Zuckerman functor due to Bernstein, which allows us to deduce the computation from a result of Hotta and Kashiwara. As a consequence we give an explicit connection between Wallach's construction of Weyl group representations and a construction due to Hotta and Kashiwara.

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