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arXiv · 1405.2626

On the Howe duality conjecture in classical theta correspondence

Wee Teck Gan·Shuichiro Takeda
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Abstract

We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for any nonarchimedean local field of characteristic not 2 and in arbitrary residual characteristic.

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Wee Teck Gan, Shuichiro Takeda. 2014-05-12. On the Howe duality conjecture in classical theta correspondence. https://arxiv.org/abs/1405.2626

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