Green Vertex Theory, Green Correspondence, and Harish-Chandra Induction

Green Theory for Hecke Algebras and Harish-chandra Philosophy

This paper can be considered as a continuation of a survey article on the representation theory of nite general linear groups in non describing characteristic D4]. The main theme there as well as in the present paper is the connection between the representation theory of quantum GL n and the non describing characteristic case for general linear groups. This connection is given through certain t...

Generalized Harish-Chandra Modules

Harish-chandra and His Work

I began to study representation theory while I was a graduate student at the University of Washington in the early seventies. At that time learning the theory of unitary representations of semisimple Lie groups primarily meant learning Harish-Chandra's work, and it was not an easy task. By that time Harish-Chandra had published over fifty papers, more than a thousand pages, on this subject. His...

Mathema Tics: Harish-chandra

Harish-chandra Vertices

The irreducible complex representations of nite groups of Lie type are divided into series by means of the Harish-Chandra philosophy, whose starting point is the concept of cuspidal characters (see e.g..Sr]). The classiication of the irreducible characters of such a group G can be done in two steps: First nd all cuspidal irreducible characters of Levi subgroups L of G. Then apply Harish-Chandra...