On the non-vanishing of theta liftings of tempered representations of   U(p,q)
  In this paper, we give an explicit determination of the non-vanishing of the theta liftings for unitary dual pairs (U(p,q), U(r,s)). Assuming the local Gan-Gross-Prasad conjecture, we determine when theta lifts of tempered representations are nonzero in terms of the local Langlands correspondence. 
Hiraku Atobe
math.RT math.NT