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.