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Zuckerman functors between equivariant derived categories


Author: Pavle Pandzic
Journal: Trans. Amer. Math. Soc. 359 (2007), 2191-2220
MSC (2000): Primary 22E46
DOI: https://doi.org/10.1090/S0002-9947-06-04013-X
Published electronically: December 19, 2006
MathSciNet review: 2276617
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Abstract: 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. This 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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Additional Information

Pavle Pandzic
Affiliation: Department of Mathematics, University of Zagreb, PP 335, 10002 Zagreb, Croatia
Email: pandzic@math.hr

DOI: https://doi.org/10.1090/S0002-9947-06-04013-X
Received by editor(s): January 15, 2004
Received by editor(s) in revised form: March 9, 2005
Published electronically: December 19, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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