On towers of liftings and hypercuspidality for unitary groups

Abstract

Given a cuspidal automorphic representation on U(2, 3), then its theta lift to U(i, i) is cuspidal. if and only if its theta lift to U(i-1, i-1) is zero. Also, the theta lift of a cuspidal generic representation from U(2, 3) to U(3, 3) is generic. The theta lift of a cuspidal representation from U(2, 3) to U(4, 4) or to U(5, 5) is hypercuspidal.