Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I
نویسنده
چکیده
The algorithm of computing generalized Green functions of a reductive group G contains some unknown scalars occurring from the Fq-structure of irreducible local systems on unipotent classes of G. In this paper, we determine such scalars in the case where G = SLn with Frobenius map F of split type or non-split type. In the case where F is of non-split type, we use the theory of graded Hecke algebras due to Lusztig.
منابع مشابه
Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, Ii
This paper is concerned with the problem of the determination of unknown scalars involved in the algorithm of computing the generalized Green functions of reductive groups G over a finite field. In the previous paper, we have treated the case where G = SLn. In this paper, we determine the scalars in the case where G is a classical group Sp2n or SON for arbitrary characteristic.
متن کاملOn 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 nite reductive group G(F q ). This is de ned in terms of certain average values of the irreducible characters on unipotent classes. The problem was solved by Lusztig [16] for the case where q is a power of a su ciently large prime. In this paper we show that, in general, these ...
متن کاملThe Space of Unipotently Supported Class Functions on a Finite Reductive Group
Let G be a connected reductive algebraic group over an algebraic closure F of the finite field Fq of q elements; assume G has an Fq-structure with associated Frobenius endomorphism F and let l be a prime distinct from the characteristic of Fq. In [DLM1, §7.1] and [DLM2] we outlined a program for the determination of the irreducible Ql-characters of the finite group G , which showed that the pro...
متن کاملGeneric Blocks of Finite Reductive Groups
To Charlie Curtis Contents 0. Introduction 1. Notation, prerequisites and complements A. Generic nite reductive groups Usual invariants of a generic nite reductive group Class functions on G d{split Levi subgroups B. Generic characters Some consequences of Lusztig's results Generic unipotent characters, uniform functions The generic Deligne{Lusztig induction and restriction 2. d{cuspidality and...
متن کاملRational Points on Generalized Flag Varieties and Unipotent Conjugacy in Finite Groups of Lie Type
Let G be a connected reductive algebraic group defined over the finite field Fq , where q is a power of a good prime for G. We write F for the Frobenius morphism of G corresponding to the Fq-structure, so that GF is a finite group of Lie type. Let P be an F -stable parabolic subgroup of G and let U be the unipotent radical of P . In this paper, we prove that the number of UF -conjugacy classes ...
متن کامل