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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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Character values, Schur indices and character sheaves
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by Meinolf Geck PDF
Represent. Theory 7 (2003), 19-55 Request permission


In this paper we are concerned with the problem of determining the character values and Schur indices of a finite group of Lie type over ${\mathbb F}_q$. We show that (under some conditions on $q$) these values lie in the ring of algebraic integers generated by $(1+ \sqrt {\pm q})/2$ and roots of unity of order prime to $q$. Furthermore, we determine the Schur indices for some of the (nonrational) unipotent characters in exceptional groups. Our results, combined with previous results due to Gow, Ohmori and Lusztig, imply that there are only 6 cases left where the Schur index of a cuspidal unipotent character remains unknown. Our methods rely, in an essential way, on Lusztig’s theory of character sheaves.
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Additional Information
  • Meinolf Geck
  • Affiliation: Institut Girard Desargues, bat. Jean Braconnier, Université Lyon 1, 21 av Claude Bernard, F–69622 Villeurbanne Cedex, France
  • MR Author ID: 272405
  • Email:
  • Received by editor(s): July 15, 2002
  • Received by editor(s) in revised form: November 13, 2002
  • Published electronically: February 19, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 19-55
  • MSC (2000): Primary 20C15; Secondary 20G40
  • DOI:
  • MathSciNet review: 1973366