Harish-Chandra cuspidal pairs

Harish-chandra Modules for Quantum Symmetric Pairs

Let U denote the quantized enveloping algebra associated to a semisimple Lie algebra. This paper studies Harish-Chandra modules for the recently constructed quantum symmetric pairs U ,B in the maximally split case. Finite-dimensional U -modules are shown to be Harish-Chandra as well as the B-unitary socle of an arbitrary module. A classification of finite-dimensional spherical modules analogous...

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...