**Date & Time:** Friday, March 21, 2014, 14:30-15:30.

**Venue:** Ramanujan Hall

**Title:** Remarks on Kostant's construction of semi-simple groups

**Speaker:** William A. Casselman, University of British Columbia

**Abstract:** The majority of the finite simple groups
are rational points on a semi-simple group defined over a finite field.
The classification of such groups is basically derived from
a famous paper by Chevalley, dating to 1955. What he did in that paper
was construct a large collection of such groups
defined by exactly the data that defines semi-simple groups over the
complex numbers. His construction was clarified a bit by
Robert Steinberg, but the most satisfactory construction is
contained in a little understood, and somewhat incomplete, paper by Bertram
Kostant dating to 1965. Recently, George Lusztig
has added details to Kostant's proposals. At the same time he
extended them to the construction of quantum groups, but in the process
obscuring the basic simplicity of Kostant's construction.
In this talk, I'll try to explain Kostant's ideas in a simpler fashion.