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


Author: Kazuki Morimoto
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11F70; Secondary 11F30
DOI: https://doi.org/10.1090/tran/7119
Published electronically: February 1, 2018
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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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Additional Information

Kazuki Morimoto
Affiliation: Department of Mathematics, Kobe University, 1-1, Rokkodai, Nada-ku, Kobe, Japan
Email: kazukimorimo@gmail.com

DOI: https://doi.org/10.1090/tran/7119
Received by editor(s): October 3, 2016
Received by editor(s) in revised form: November 3, 2016
Published electronically: February 1, 2018
Additional Notes: The research of the author was supported in part by Grant-in-Aid for JSPS Fellow (26-1158) and Grant-in-Aid for Young Scientists (B) 26800021.
Article copyright: © Copyright 2018 American Mathematical Society

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