The set of local 𝐴-packets containing a given representation

Author:

Atobe Hiraku1

Affiliation:

1. Department of Mathematics , Hokkaido University , Kita 10, Nishi 8, Kita-Ku , Sapporo , Hokkaido, 060-0810 , Japan

Abstract

Abstract In this paper, we give an algorithm to determine all local 𝐴-packets containing a given irreducible representation of a split special odd orthogonal group or a symplectic group over a 𝑝-adic field. Especially, we can determine whether a given irreducible representation is of Arthur type or not.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

1. J. Arthur, The endoscopic classification of representations. Orthogonal and symplectic groups, Amer. Math. Soc. Colloq. Publ. 61, American Mathematical Society, Providence 2013.

2. H. Atobe, Construction of local 𝐴-packets, J. reine angew. math. 790 (2022), 1–51.

3. H. Atobe, On the socles of certain parabolically induced representations of 𝑝-adic classical groups, Represent. Theory 26 (2022), 515–541.

4. H. Atobe and A. Mínguez, The explicit Zelevinsky–Aubert duality, Compos. Math. 159 (2023), no. 2, 380–418.

5. W. T. Gan, B. H. Gross and D. Prasad, Symplectic local root numbers, central critical 𝐿 values, and restriction problems in the representation theory of classical groups, Sur les conjectures de Gross et Prasad. I, Astérisque 346, Société Mathématique de France, Paris (2012), 1–109.

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Weak Local Arthur Packets Conjecture for Split Classical Groups;International Mathematics Research Notices;2024-05-17

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