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Cohomology of standard modules on partial flag varieties

Author: S. N. Kitchen
Journal: Represent. Theory 16 (2012), 317-344
MSC (2010): Primary 22-xx
Published electronically: July 11, 2012
MathSciNet review: 2945222
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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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S. N. Kitchen
Affiliation: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstr. 1, 79104 Freiburg im Breisgau, Germany

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.