Bounding Harish-Chandra series

Macdonald Difference Operators and Harish-chandra Series

We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik’s commuting algebra of difference operators via an analog of the Harish-Chandra isomorphism. Analogs of Harish-Chandra series are defined and realized as solutions to the system of basic hypergeometric difference equatio...

Generalized Harish-Chandra Modules

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...

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...