On the average values of the irreducible characters of finite groups of Lie type on geometric unipotent classes
In 1980, Lusztig posed the problem of showing the existence of a unipotent support for the irreducible characters of a finite reductive group . This is defined in terms of certain average values of the irreducible characters on unipotent classes. The problem was solved by Lusztig  for the case where is a power of a sufficiently large prime. In this paper we show that, in general, these average values can be expressed in terms of the Green functions of . In good characteristic, these Green functions are given by polynomials in . Combining this with Lusztig's results, we can then establish the existence of unipotent supports whenever is a power of a good prime.
Cite this article
Meinolf Geck, On the average values of the irreducible characters of finite groups of Lie type on geometric unipotent classes. Doc. Math. 1 (1996), pp. 293–317DOI 10.4171/DM/15