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Spherical functions of the symmetric space $G(\mathbb{F} _{q^{2}})/G(\mathbb{F} _q)$

Author: Anthony Henderson
Journal: Represent. Theory 5 (2001), 581-614
MSC (2000): Primary 20G40, 20G05; Secondary 20C15, 32C38
Published electronically: November 28, 2001
MathSciNet review: 1870603
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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

Keywords: Algebraic groups, perverse sheaves
Received by editor(s): December 1, 2000
Received by editor(s) in revised form: August 14, 2001
Published electronically: November 28, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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