On the Howe duality conjecture in classical theta correspondence

By W. Gan, Shuichiro Takeda. 2014

47 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d1f31368cb236cbc6da1d552815462648bc026fd

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In Geometry and Topology

1. Hiraku Atobe
2. W. Gan
3. Manjul Bhargava
4. Atsushi Ichino
5. Ralf Schmidt
6. Shuichiro Takeda

In Mathematical Physics

1. Hiraku Atobe
2. W. Gan
3. Atsushi Ichino
4. Manjul Bhargava
5. Shuichiro Takeda
6. Ralf Schmidt
7. Michael Rapoport

Citations in the corpus

• Local theta correspondence of tempered representations and Langlands parameters (2016, methodology): “e can interchange τiwith τ1 (see e.g., [Z]). Hence we have τi= χWStl+1 for any i= 1,...,r. The following is the key result. Proposition 6.16. We have r= 1. Proof. By (the proof of) Proposition 3.1 in [GT1], we can find an irreducible representation σ1 of H(Vm 1) such that IndH(Vm) Q(Yl+1) (χWStl+1|·|”