Spherical functions of the symmetric space 𝐺(𝔽_{𝕢²})/𝔾(𝔽_{𝕢})

Henderson, Anthony

doi:10.1090/S1088-4165-01-00119-4

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.

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