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arXiv · 0903.1418

Dual pairs and contragredients of irreducible representations

Binyong Sun
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Abstract

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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Binyong Sun. 2009-03-08. Dual pairs and contragredients of irreducible representations. https://arxiv.org/abs/0903.1418

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