Tempered representations and the theta correspondence

http://dx.doi.org/10.4153/CJM-1998-053-6
Canad. J. Math. 50(1998), 1105-1118

  Published:1998-10-01
 Printed: Oct 1998

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 $\pi$.