SPHERICAL FUNCTIONS OF THE SYMMETRIC SPACE G ( F q 2 ) / G ( F q )
نویسنده
چکیده
We apply Lusztig’s theory of character sheaves to the problem of calculating the spherical functions of G(Fq2 )/G(Fq), 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 = GLn. The proof includes a result about convolution of character sheaves and its interaction with the associated two-sided cells. 0. Introduction Let Γ be a finite group and τ : Γ → Γ a nontrivial group involution. Let Γ be the fixed-point subgroup. Then the quotient set Γ/Γ is called a finite symmetric space. For any function f : Γ→ Q, we write Ave(f) for the function on Γ/Γ given by averaging over the coset Ave(f)(γΓ ) = 1 |Γτ | ∑
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