Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Representation Theory
Representation Theory
ISSN 1088-4165

 

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
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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22-xx

Retrieve articles in all journals with MSC (2010): 22-xx


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

DOI: http://dx.doi.org/10.1090/S1088-4165-2012-00419-8
PII: S 1088-4165(2012)00419-8
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.