On Unitary Representations of GL2n Distinguished by the Symplectic Group

Details On Unitary Representations of GL2n Distinguished by the Symplectic Group On Unitary Representations of GL2n Distinguished by the Symplectic Group

2008-06-25

arxiv.org/abs/0806.4031v1

Journal of Number Theory No.125, 2007

Mathematics

Representation Theory

Two references added and minor editing of the published version

Scientific paper

We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a result of M. Heumos and S. Rallis our methods, unlike their purely local technique, re- lies on the theory of automorphic forms. The results of this paper together with later works by the authors imply that the family of representations studied in this paper contains all irreducible, unitary representations of the general linear group that are distin- guished by the symplectic group.

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