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Theta Lifts of Tempered Representations for Dual Pairs (Sp2n,O(V))
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- Journal:
- Canadian Journal of Mathematics / Volume 60 / Issue 6 / 01 December 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1306-1335
- Print publication:
- 01 December 2008
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- Article
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This paper is the continuation of our previous work on the explicit determination of the structure of theta lifts for dual pairs
$\left( {{\text{S}}_{{{\text{p}}_{2n}},}}\,O\left( V \right) \right)$ over a non-archimedean field 
$F$ of characteristic different than 2, where 
$n$ is the split rank of 
${{\text{S}}_{{{\text{p}}_{2n}}}}$ and the dimension of the space 
$V$ (over $F$) is even. We determine the structure of theta lifts of tempered representations in terms of theta lifts of representations in discrete series.
