Abstract
Let G be a finite Chevalley group. We are concerned with computing the values of the unipotent characters of G by making use of Lusztig's theory of character sheaves. In this framework, one has to find the transformation between several bases for the class functions on G. In principle, this has been achieved by Lusztig and Shoji, but the underlying process involves some scalars which are still unknown in many cases. We shall determine these scalars in the specific case where G is one of the groups E6(q), E62(q), and q is a power of the bad prime p=3 for E6, by exploiting known facts about the representation theory of the Hecke algebra associated with G.
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