Equivariant analogues of Zuckerman functors

Details Equivariant analogues of Zuckerman functors Equivariant analogues of Zuckerman functors

2004-01-11

arxiv.org/abs/math/0401106v2

Mathematics

Representation Theory

37 pages; added reference

Scientific paper

We review the Beilinson-Ginzburg construction of equivariant derived categories of Harish-Chandra modules, and introduce analogues of Zuckerman functors in this setting. They are given by an explicit formula, which works equally well in the case of modules with a given infinitesimal character, which is important if one wants to apply Beilinson-Bernstein localization. We also show how to recover the usual Zuckerman functors from the equivariant ones by passing to cohomology.

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