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.
