On the Howe duality conjecture in classical theta correspondence
  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. 
Wee Teck Gan and Shuichiro Takeda
math.NT math.RT