Generalized Green functions and unipotent classes for finite reductive groups, I

Details Generalized Green functions and unipotent classes for finite reductive groups, I Generalized Green functions and unipotent classes for finite reductive groups, I

2005-07-04

arxiv.org/abs/math/0507057v1

Mathematics

Representation Theory

36 pages

Scientific paper

The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the F_q structure of irreducible local systems on unipotent classes on G. In this paper, we determine such scalars in the case where G = SL_n with Frobenius map F of split or non-split type. In the case where F is of non-split type, we use the theory of graded Hecke algebras and their representations on the equivariant homology group due to Lusztig.

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