On the non-vanishing of theta liftings of tempered representations of U(p,q)

TL;DR

This paper explicitly determines when theta liftings of tempered representations of unitary groups are non-zero, assuming the local Gan-Gross-Prasad conjecture, by linking to the local Langlands correspondence.

Contribution

It provides an explicit criterion for the non-vanishing of theta liftings of tempered representations of U(p,q) under the assumption of the local Gan-Gross-Prasad conjecture.

Findings

Explicit non-vanishing criteria for theta liftings.

Connection established between theta liftings and local Langlands correspondence.

Conditional results assuming the local Gan-Gross-Prasad conjecture.

Abstract

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.