Linear periods for unitary representations

Abstract

Let $F$ be a local non-Archimedean field of characteristic zero with a finite residue field. Based on Tadić's classification of the unitary dual of ${\mathrm{GL}}_{2n}(F)$, we classify irreducible unitary representations of ${\mathrm{GL}}_{2n}(F)$ that have nonzero linear periods, in terms of Speh representations that have nonzero periods. We also give a necessary and sufficient condition for the existence of a nonzero linear period for a Speh representation.

34 pages, 2 figures. Comments are welcome! Fix some errors (those related to Lemma 3.1 (2) in the first version). Final version to appear in Math Z

References in corpus (1)

• Branching laws for Classical Groups: the non-tempered case