On (χ,b)-factors of cuspidal automorphic representations of unitary groups I

Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations σ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψ_σ associated to σ, 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 (χ, 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].