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International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn005, 166 pages, doi:10.1093/imrp/rpn005 published on June 4, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Distinguished Tame Supercuspidal Representations

Jeffrey Hakim1 and Fiona Murnaghan2

1 Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue NW, Washington, DC 20016
2 Department of Mathematics, University of Toronto, 40 Saint George Street, Toronto, Canada M5S 2E4

Correspondence: Correspondence to be sent to: jhakim{at}american.edu

This paper studies the behavior of Jiu-Kang Yu's tame supercuspidal representations relative to involutions of reductive p-adic groups. Symmetric space methods are used to illuminate various aspects of Yu's construction. Necessary conditions for a tame supercuspidal representation of G to be distinguished by (the fixed points of) an involution of G are expressed in terms of properties of the G-orbit of the associated G-datum. When these conditions are satisfied, the question of whether a tame supercuspidal representation is distinguished reduces to the question of whether certain cuspidal representations of finite groups of Lie type are distinguished relative to particular quadratic characters. As an application of the main results, we obtain necessary and sufficient conditions for equivalence of two of Yu's supercuspidal representations associated to distinct G-data.



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This Article
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