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# Tempered representations and the theta correspondence

Published:1998-10-01
Printed: Oct 1998
• Brooks Roberts
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## Abstract

Let $V$ be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field $F$ of characteristic zero, and let $n$ be a nonnegative integer. Suppose that $\sigma \in \Irr \bigl(\OO (V)\bigr)$ and $\pi \in \Irr \bigl(\Sp (n,F)\bigr)$ correspond under the theta correspondence. Assuming that $\sigma$ is tempered, we investigate the problem of determining the Langlands quotient data for $\pi$.
 MSC Classifications: 11F27 - Theta series; Weil representation; theta correspondences 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]