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Representation Theory
Representation Theory
ISSN 1088-4165

 

Tempered representations and nilpotent orbits


Author: Benjamin Harris
Journal: Represent. Theory 16 (2012), 610-619
MSC (2010): Primary 22E46; Secondary 43A65, 22E45
Published electronically: December 13, 2012
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Abstract: Given a nilpotent orbit $ \mathcal {O}$ of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation $ \pi $ such that $ \mathcal {O}$ occurs in the wave front cycle of $ \pi $. The coefficients of the wave front cycle of a tempered representation are expressed in terms of volumes of precompact submanifolds of an affine space.


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Additional Information

Benjamin Harris
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: blharris@math.mit.edu

DOI: http://dx.doi.org/10.1090/S1088-4165-2012-00414-9
PII: S 1088-4165(2012)00414-9
Keywords: Tempered representation, discrete series representation, wave front cycle, associated variety, reductive lie group, real reductive algebraic group, nilpotent orbit, distinguished nilpotent orbit, noticed nilpotent orbit, coadjoint orbit
Received by editor(s): October 19, 2010
Received by editor(s) in revised form: May 28, 2011, and September 18, 2011
Published electronically: December 13, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.