Cohomology of standard modules on partial flag varieties

Author:
S. N. Kitchen

Journal:
Represent. Theory **16** (2012), 317-344

MSC (2010):
Primary 22-xx

DOI:
https://doi.org/10.1090/S1088-4165-2012-00419-8

Published electronically:
July 11, 2012

MathSciNet review:
2945222

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Cohomological induction gives an algebraic method for constructing representations of a real reductive Lie group $G$ from irreducible representations of reductive subgroups. Beilinson-Bernstein localization alternatively gives a geometric method for constructing Harish-Chandra modules for $G$ from certain representations of a Cartan subgroup. The duality theorem of Hecht, Miličić, Schmid and Wolf establishes a relationship between modules cohomologically induced from minimal parabolics and the cohomology of the $\mathscr {D}$-modules on the complex flag variety for $G$ determined by the Beilinson-Bernstein construction. The main results of this paper give a generalization of the duality theorem to partial flag varieties, which recovers cohomologically induced modules arising from nonminimal parabolics.

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Additional Information

**S. N. Kitchen**

Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstr. 1, 79104 Freiburg im Breisgau, Germany

Email:
sarah.kitchen@math.uni-freiburg.de

Received by editor(s):
February 7, 2011

Received by editor(s) in revised form:
January 20, 2012, and February 24, 2012

Published electronically:
July 11, 2012

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.