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

 

Distinguished tame supercuspidal representations and odd orthogonal periods


Authors: Jeffrey Hakim and Joshua Lansky
Journal: Represent. Theory 16 (2012), 276-316
MSC (2010): Primary 22E50, 11F70; Secondary 11F67, 11E08, 11E81
Published electronically: June 1, 2012
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We further develop and simplify the general theory of distinguished tame supercuspidal representations of reductive $ p$-adic groups due to Hakim and Murnaghan, as well as the analogous theory for finite reductive groups due to Lusztig. We apply our results to study the representations of $ \mathrm {GL}_n(F)$, with $ n$ odd and $ F$ a nonarchimedean local field, that are distinguished with respect to an orthogonal group in $ n$ variables. In particular, we determine precisely when a supercuspidal representation is distinguished with respect to an orthogonal group and, if so, that the space of distinguishing linear forms has dimension one.


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


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E50, 11F70, 11F67, 11E08, 11E81

Retrieve articles in all journals with MSC (2010): 22E50, 11F70, 11F67, 11E08, 11E81


Additional Information

Jeffrey Hakim
Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
Email: jhakim@american.edu

Joshua Lansky
Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
Email: lansky@american.edu

DOI: http://dx.doi.org/10.1090/S1088-4165-2012-00418-6
PII: S 1088-4165(2012)00418-6
Keywords: Supercuspidal representation, involution, distinguished representation, orthogonal group.
Received by editor(s): March 7, 2011
Received by editor(s) in revised form: November 23, 2011
Published electronically: June 1, 2012
Additional Notes: Both authors were supported by NSF grant DMS-0854844.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.