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

Morimoto, Kazuki

doi:10.1090/tran/7119

On the irreducibility of global descents for even unitary groups and its applications
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Trans. Amer. Math. Soc. 370 (2018), 6245-6295 Request permission

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 $\mathrm {U}(n,n)(\mathbb {A})$ and a certain set of irreducible square-integrable automorphic representations of $\mathrm {U}(2n, 2n)(\mathbb {A})$. 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 $\mathrm {U}(n,n)$. 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 $\mathrm {U}(n,n)$.

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