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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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Spherical functions of the symmetric space $G(\mathbb {F}_{q^{2}})/G(\mathbb {F}_q)$
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by Anthony Henderson PDF
Represent. Theory 5 (2001), 581-614 Request permission

Abstract:

We apply Lusztig’s theory of character sheaves to the problem of calculating the spherical functions of $G(\mathbb {F}_{q^{2}})/G(\mathbb {F}_q)$, where $G$ is a connected reductive algebraic group. We obtain the solution for generic spherical functions for any $G$, and for all spherical functions when $G=GL_n$. The proof includes a result about convolution of character sheaves and its interaction with the associated two-sided cells.
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Additional Information
  • Anthony Henderson
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Address at time of publication: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
  • MR Author ID: 687061
  • ORCID: 0000-0002-3965-7259
  • Email: anthonyh@maths.usyd.edu.au
  • Received by editor(s): December 1, 2000
  • Received by editor(s) in revised form: August 14, 2001
  • Published electronically: November 28, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 581-614
  • MSC (2000): Primary 20G40, 20G05; Secondary 20C15, 32C38
  • DOI: https://doi.org/10.1090/S1088-4165-01-00119-4
  • MathSciNet review: 1870603