On Fourier coefficients of certain residual representations of symplectic groups

Abstract

In the theory of automorphic descents developed by Ginzburg, Rallis and Soudry in [GRS11], the structure of Fourier coefficients of the residual representations of certain special Eisenstein series plays important roles. Started from [JLZ13], the authors are looking for more general residual representations, which may yield more general theory of automorphic descents. In this paper, we investigate the structure of Fourier coefficients of certain residual representations of symplectic groups, corresponding to certain interesting families of global Arthur parameters. On one hand, the results partially confirm a conjecture proposed by the first named author in [J14] on relations between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. On the other hand, the results of this paper can be regarded as a first step towards more general automorphic descents for symplectic groups, which will be considered in our future work.

44 pages. Final version. To appear in Pacific J. of Math

References in corpus (4)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• On Extension of Ginzburg-Jiang-Soudry Correspondence to Certain Automorphic Forms on $Sp_{4mn}(\BA)$ and $\wt{Sp}_{4mn \pm 2n}(\BA)$
• Fourier coefficients for automorphic forms on quasisplit classical groups
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Cited by in corpus (2)

• Doubling Constructions and Tensor Product $L$-Functions: coverings of the symplectic group
• On cuspidality of global Arthur packets for symplectic groups