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Semisimple characters for inner forms II: Quaternionic forms of $ p$-adic classical groups ($ p$ odd)


Author: Daniel Skodlerack
Journal: Represent. Theory 24 (2020), 323-359
MSC (2010): Primary 11E57, 11E95, 20G05, 22E50
DOI: https://doi.org/10.1090/ert/544
Published electronically: July 29, 2020
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Abstract: In this article we consider the set $ G$ of rational points of a quaternionic form of a symplectic or an orthogonal group defined over a non-
Archimedean local field of odd residue characteristic. We construct all full self-dual semisimple characters for $ G$ and we classify their intertwining classes using endo-parameters. We compute the set of intertwiners between self-dual semisimple characters, and prove an intertwining and conjugacy theorem. Finally we count all $ G$-intertwining classes of full self-dual semisimple characters which lift to the same $ \tilde {G}$-intertwining class of a full semisimple character for the ambient general linear group $ \tilde {G}$ for $ G$.


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Additional Information

Daniel Skodlerack
Affiliation: Institute of Mathematical Sciences, ShanghaiTech University, 393 Huaxia Middle Road, Pudong, People’s Republic of China, 201210
Email: dskodlerack@shanghaitech.edu.cn

DOI: https://doi.org/10.1090/ert/544
Received by editor(s): August 16, 2018
Received by editor(s) in revised form: January 26, 2020
Published electronically: July 29, 2020
Article copyright: © Copyright 2020 American Mathematical Society