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Tame Supercuspidal Representations of GL(n) Distinguished by a Unitary Group

Published online by Cambridge University Press:  04 December 2007

Jeffrey Hakim  and
Fiona Murnaghan
Jeffrey Hakim
Affiliation:
Department of Mathematics and Statistics, American University, Washington, DC 20016-8050, U.S.A. e-mail: jhakim@american.edu Research supported in part by NSA grant #MDA904-99-1-0065.
Fiona Murnaghan
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada, M5S 3G3 Research supported in part by NSERC
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Abstract

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This paper analyzes the space HomH(π, 1), where π is an irreducible, tame supercuspidal representation of GL(n) over a p-adic field and H is a unitary group in n variables contained in GL(n). It is shown that this space of linear forms has dimension at most one. The representations π which admit nonzero H-invariant linear forms are characterized in several ways, for example, as the irreducible, tame supercuspidal representations which are quadratic base change lifts.

Keywords

supercupsoidal representationsdistinguished representationsquadratic base change
Type
Research Article
Information
Compositio Mathematica , Volume 133 , Issue 2 , September 2002 , pp. 199 - 244
Copyright
© 2002 Kluwer Academic Publishers