Dual pairs and contragredients of irreducible representations

Details Dual pairs and contragredients of irreducible representations Dual pairs and contragredients of irreducible representations

2009-03-08

arxiv.org/abs/0903.1418v2

Pacific. J. Math., 249 (2011), 485--494

Mathematics

Representation Theory

Scientific paper

Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient of $\pi$ is isomorphic to a twist of $\pi$ by an automorphism of $G$. We prove a similar result for double covers of $G$ which occur in the study of local theta correspondences.

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