Symplectic-Whittaker models for Gl_n

Michael Justin Heumos and Stephen James Rallis

Vol. 146 (1990), No. 2, 247–279

DOI: 10.2140/pjm.1990.146.247

Abstract

We consider the Klyachko models of admissible irreducible representations of the group GL_n(F) where F is a non-Archimedean local field of characteristic 0. These are models which generalize the usual Whittaker model by allowing the inducing subgroup a symplectic component. We prove the uniqueness of the symplectic models and the disjointness for unitary representations of the different models. Moreover, for n ≤ 4 we prove that all unitary irreducible representations admit a Klyachko model.

Mathematical Subject Classification 2000

Primary: 22E50

Milestones

Received: 9 December 1988

Revised: 24 October 1989

Published: 1 December 1990