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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Cohomology of standard modules on partial flag varieties
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by S. N. Kitchen PDF
Represent. Theory 16 (2012), 317-344 Request permission


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:
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 16 (2012), 317-344
  • MSC (2010): Primary 22-xx
  • DOI:
  • MathSciNet review: 2945222