Representation Theory

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

Author(s): Anthony Henderson
Journal: Represent. Theory 5 (2001), 581-614.
MSC (2000): Primary 20G40, 20G05; Secondary 20C15, 32C38
Posted: 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

is a connected reductive algebraic group. We obtain the solution for generic spherical functions for any

, and for all spherical functions when

. The proof includes a result about convolution of character sheaves and its interaction with the associated two-sided cells.

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