Vol. 249, No. 2, 2011

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Dual pairs and contragredients of irreducible representations

Binyong Sun

Vol. 249 (2011), No. 2, 485–494

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.

contragredient representation, dual pair, irreducible representation
Mathematical Subject Classification 2000
Primary: 22E35, 22E46
Received: 7 December 2009
Revised: 21 April 2010
Accepted: 10 May 2010
Published: 1 February 2011
Binyong Sun
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing 100190