On representations of GL 2n (F) with a symplectic period
Abstract
The main aim of this paper is to classify the irreducible admissible representations of
GL
4
(F)
and
GL
6
(F)
for a nonarchimedean local field
F
, which bear a nontrivial linear form invariant under the groups
Sp
4
(F)
and
Sp
6
(F)
respectively. We propose a few conjectures for the general case.