On the irreducibility of global descents for even unitary groups and its applications

Abstract

In this paper, we prove the irreducibility of global descents for even unitary groups. More generally, through Fourier-Jacobi coefficients of automorphic forms, we give a bijection between a certain set of irreducible cuspidal automorphic representations of U ( n , n ) ( A ) \mathrm {U}(n,n)(\mathbb {A}) and a certain set of irreducible square-integrable automorphic representations of U ( 2 n , 2 n ) ( A ) \mathrm {U}(2n, 2n)(\mathbb {A}) . We also give three applications of the irreducibility of global descents. As a global application, we prove a rigidity theorem for irreducible generic cuspidal automorphic representations of U ( n , n ) \mathrm {U}(n,n) . Moreover, as a local application, we prove the irreducibility of explicit local descents for a couple of supercuspidal representations and a local converse theorem for generic representations in the case of U ( n , n ) \mathrm {U}(n,n) .