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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
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.

Type
Research Article
Copyright
© 2002 Kluwer Academic Publishers