Compositio Mathematica

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

Jeffrey Hakim a1a2 and Fiona Murnaghan a3a4
a1 Department of Mathematics and Statistics, American University, Washington, DC 20016-8050, U.S.A. e-mail:
a2 Research supported in part by NSA grant #MDA904-99-1-0065.
a3 Department of Mathematics, University of Toronto, Toronto, Canada, M5S 3G3
a4 Research supported in part by NSERC

Article author query
hakim j   [Google Scholar] 
murnaghan f   [Google Scholar] 


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.

Key Words: supercupsoidal representations; distinguished representations; quadratic base change.