Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Subfield symmetric spaces for finite special linear groups
HTML articles powered by AMS MathViewer

by Toshiaki Shoji and Karine Sorlin
Represent. Theory 8 (2004), 487-521
Published electronically: November 15, 2004


Let $G$ be a connected algebraic group defined over a finite field ${\mathbf F}_q$. For each irreducible character $\rho$ of $G(\mathbf F_{q^r})$, we denote by $m_r(\rho )$ the multiplicity of $1_{G({\mathbf F}_q)}$ in the restriction of $\rho$ to $G({\mathbf F}_q)$. In the case where $G$ is reductive with connected center and is simple modulo center, Kawanaka determined $m_2(\rho )$ for almost all cases, and then Lusztig gave a general formula for $m_2(\rho )$. In the case where the center of $G$ is not connected, such a result is not known. In this paper we determine $m_2(\rho )$, up to some minor ambiguity, in the case where $G$ is the special linear group.

We also discuss, for any $r \ge 2$, the relationship between $m_r(\rho )$ with the theory of Shintani descent in the case where $G$ is a connected algebraic group.

Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 20G40, 20G05
  • Retrieve articles in all journals with MSC (2000): 20G40, 20G05
Bibliographic Information
  • Toshiaki Shoji
  • Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
  • Karine Sorlin
  • Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
  • Address at time of publication: LAMFA, Université de Picardie-Jules Verne, 33 rue Saint-Leu, 80039 Amiens Cedex, France
  • Received by editor(s): March 2, 2004
  • Received by editor(s) in revised form: September 13, 2004
  • Published electronically: November 15, 2004
  • Additional Notes: The second author would like to thank the JSPS for support which made this collaboration possible
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 8 (2004), 487-521
  • MSC (2000): Primary 20G40; Secondary 20G05
  • DOI:
  • MathSciNet review: 2110358