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

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- by Anthony Henderson
- Represent. Theory
**5**(2001), 581-614 - DOI: https://doi.org/10.1090/S1088-4165-01-00119-4
- Published electronically: November 28, 2001
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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.## References

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## Bibliographic 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