Generalized Green functions and unipotent classes for finite reductive groups, I
Abstract
The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the Fq structure of irreducible local systems on unipotent classes on G. In this paper, we determine such scalars in the case where G = SLn 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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