Dual pairs and contragredients of irreducible representations

Binyong Sun

Vol. 249 (2011), No. 2, 485–494

DOI: 10.2140/pjm.2011.249.485

Abstract

Let G be one of the classical groups GL(n), U(n), O(n) or Sp(2n), over a nonarchimedean local field of characteristic zero. It is well known that the contragredient of an irreducible admissible smooth representation of G is isomorphic to a twist of it by an automorphism of G. We prove that similar results hold for double covers of G that occur in the study of local theta correspondences.

Keywords

contragredient representation, dual pair, irreducible representation

Mathematical Subject Classification 2000

Primary: 22E35, 22E46

Milestones

Received: 7 December 2009

Revised: 21 April 2010

Accepted: 10 May 2010

Published: 1 February 2011