Finite reductive groups (Q2707647)

This paper consists of a chapter from the proceeding of the summer school on ``representation theory of algebras, finite and reductive groups'', Cluj-Napoca, ``Babeş Bolyai'' University, 1998. The aim of this chapter is to give an introduction to the theory of finite groups of Lie type and their ordinary representations. This is best done in the framework of reductive algebraic groups. The paper explains some of the basic background material from algebraic geometry and the theory of algebraic groups and how this can be used to obtain information about representations of groups of Lie type. The paper also discusses the theory of Hecke algebras in the simplest possible case and presents some important results in this direction such as Iwahori's theorem and Tits' deformation theorem.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00029].