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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Semisimple characters for inner forms II: Quaternionic forms of $p$-adic classical groups ($p$ odd)
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by Daniel Skodlerack PDF
Represent. Theory 24 (2020), 323-359 Request permission

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
  • MR Author ID: 1033529
  • Email: dskodlerack@shanghaitech.edu.cn
  • Received by editor(s): August 16, 2018
  • Received by editor(s) in revised form: January 26, 2020
  • Published electronically: July 29, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 323-359
  • MSC (2010): Primary 11E57, 11E95, 20G05, 22E50
  • DOI: https://doi.org/10.1090/ert/544
  • MathSciNet review: 4128451