Local Theta correspondence of Tempered Representations and Langlands   parameters
  In this paper, we give an explicit determination of the theta lifting for symplectic-orthogonal and unitary dual pairs over a nonarchimedean field $F$ of characteristic $0$. We determine when theta lifts of tempered representations are nonzero, and determine the theta lifts in terms of the local Langlands correspondence. 
Hiraku Atobe and Wee Teck Gan
math.NT math.RT