One-Dimensional Representations of U (p,q) and the Howe Correspondence

We explicitly determine the theta lifts of all one-dimensional representations of U (p,q) in terms of Langlands parameters, and determine exactly which lifts are unitary. Moreover, we show that such a lift is unitary if and only if it is a weakly fair derived functor module of the form Aq(λ). Finally, we show that the correspondence of unitary representations behaves well with respect to associated cycles.