Uniqueness of generalized Waldspurger model for GL(2n)

Jiandong Guo

Vol. 180 (1997), No. 2, 273–289

DOI: 10.2140/pjm.1997.180.273

Abstract

Let E∕F be a quadratic extension of non-archimedean local field and let G be an inner form of GL(2n,F) over F, which contains a subgroup H isomorphic to GL(n,E). In this paper we prove that (G,H) is a Gelfand pair, i.e., the H-invariant linear functional, if there exists one, on the space of an irreducible admissible representation of G is unique up to a scalar. Globally this result will play an important role in the study of H-period integrals of cusp forms on G, and its relations to the special values of automorphic L-functions.

Milestones

Received: 30 January 1996

Revised: 22 May 1996

Published: 1 October 1997