On $(\chi ,b)$-factors of Cuspidal Automorphic Representations of Unitary Groups I

Abstract

Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations $\sigma$ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter $(\chi ,b)$ in the global Arthur parameter ${\psi }_{\sigma }$ associated to $\sigma$, by the endoscopic classification of Arthur ([Art13], [Mok13], [KMSW14]). The argument uses the theory of theta correspondence. This can be viewed as a part of the $(\chi ,b)$-theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain $L$-functions, which was outlined in [Ral91].

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• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• Irreducibility of Theta Lifting for Unitary Groups
• Periods and $(\chi ,b)$-factors of Cuspidal Automorphic Forms of Symplectic Groups
• Picard groups of Siegel modular threefolds and theta lifting
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Cited by in corpus (2)

• Periods and $(\chi ,b)$-factors of Cuspidal Automorphic Forms of Symplectic Groups
• Periods and $(\chi ,b)$-factors of Cuspidal Automorphic Forms of Metaplectic Groups