Nonarchimedean components of non-endoscopic automorphic representations for quasisplit Sp(N) and O(N)

Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs ( ϕ , b ) , where ϕ is an irreducible unitary cuspidal autom...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 297; no. 1-2; pp. 885 - 921
Main Author Xu, Bin
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021
Springer Nature B.V
Subjects
Endoscopy
Mathematics
Mathematics and Statistics
Number theory
Representations
Jacquet functor
Arthur packet
Symplectic and orthogonal group
Primary 22E50
Secondary 11F70
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Summary:Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs ( ϕ , b ) , where ϕ is an irreducible unitary cuspidal automorphic representation of some general linear group and b is an integer. In this paper, we study the local components of these automorphic representations at a nonarchimedean place, and we give a complete description of them in terms of their Langlands parameters.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02539-z