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On unitary representations of [formula omitted]distinguished by the symplectic group

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
125
Issue
2
Identifiers
DOI: 10.1016/j.jnt.2006.10.018

Abstract

Abstract We provide a family of representations of GL n over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp ( n ) -distinguished). This is a generalization of a result of Heumos–Rallis. Our proof uses global methods. The results of [Omer Offen, Eitan Sayag, Global mixed periods and local Klyachko models for the general linear group, submitted for publication] imply that the family at hand contains all irreducible, unitary representations that are distinguished by the symplectic group.

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