On the Howe duality conjecture in classical theta correspondence. (English) Zbl 1418.11073
Jiang, Dihua (ed.) et al., Advances in the theory of automorphic forms and their \(L\)-functions. Workshop in honor of James Cogdell’s 60th birthday, Erwin Schrödinger Institute (ESI), University of Vienna, Vienna, Austria, October 16–25, 2013. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 664, 105-117 (2016).
Summary: 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.
For the entire collection see [Zbl 1341.11002].
For the entire collection see [Zbl 1341.11002].
MSC:
| 11F27 | Theta series; Weil representation; theta correspondences |
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
