Götz Pfeiffer

CHEVIE — A system for computing and processing generic character tables

CHEVIE is a computer algebra package which collects data and programs for the representation theory of finite groups of Lie type and associated structures. We explain the theoretical and conceptual background of the various parts of CHEVIE and we show the usage of the system by means of explicit examples. More precisely, we have sections on Weyl groups and Iwahori-Hecke algebras, generic character tables of series of finite groups of Lie type, and cyclotomic algebras.

The subgroups of {

Let G be a finite group. The table of marks of G arises from a characterization of the permutation representations of G by certain numbers of fixed points. It provides a compact description of the subgroup lattice of G and enables explicit calculations in the Burnside ring of G. In this article we introduce a method for constructing the table of marks of G from tables of marks of proper subgroups of G. An implementation of this method is available in the GAP language. These computer programs are used to construct the table of marks of the sporadic simple Mathieu group M24. The final section describes how to derive information about the structure of G from its table of marks via the investigation of certain Mobius functions and the idempotents of the Burnside ring of G. Tables with detailed information about M24 and other groups are included.

M\sb {24}

Abstract. Let

}, or how to compute the table of marks of a finite group

S

GROUPS AND ACTIONS IN TRANSFORMATION SEMIGROUPS

be a transformation semigroup of degree

On Reflection Subgroups of Finite Coxeter Groups

n

Computing Transformation Semigroups

. To each element

The p-Modular Descent Algebras

s\in S

Finding Possible Permutation Characters

we associate a permutation group

A note on element centralizers in finite Coxeter groups

G_R(s)