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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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Evaluating characteristic functions of character sheaves at unipotent elements
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by Jay Taylor PDF
Represent. Theory 18 (2014), 310-340 Request permission


Assume $\mathbf {G}$ is a connected reductive algebraic group defined over an algebraic closure $\mathbb {K} = \overline {\mathbb {F}}_p$ of the finite field of prime order $p>0$. Furthermore, assume that $F : \mathbf {G} \to \mathbf {G}$ is a Frobenius endomorphism of $\mathbf {G}$. In this article we give a formula for the value of any $F$-stable character sheaf of $\mathbf {G}$ at a unipotent element. This formula is expressed in terms of class functions of $\mathbf {G}^F$ which are supported on a single unipotent class of $\mathbf {G}$. In general these functions are not determined, however, we give an expression for these functions under the assumption that $Z(\mathbf {G})$ is connected, $\mathbf {G}/Z(\mathbf {G})$ is simple and $p$ is a good prime for $\mathbf {G}$. In this case our formula is completely explicit.
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Additional Information
  • Jay Taylor
  • Affiliation: FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
  • MR Author ID: 1029591
  • ORCID: 0000-0002-9143-6605
  • Email:
  • Received by editor(s): February 5, 2014
  • Received by editor(s) in revised form: September 12, 2014
  • Published electronically: October 17, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Represent. Theory 18 (2014), 310-340
  • MSC (2010): Primary 20C33; Secondary 20G40
  • DOI:
  • MathSciNet review: 3269461