Representation Theory Seminar

Anthony McCormick, Pure Mathematics, University of Waterloo

"Algebraic Groups"

My eventual goal in this seminar is to provide some intuition for the tools used in the theory of algebraic groups and their representations. More precisely, I hope that by the end of the term we'll be comfortable with things like Borel/Cartan subalgebras (along with Borel subgroups and maximal tori), roots, weights, Dynkin diagrams, the orbit method and maybe some Lie algebra cohomology. Along the way, I would also like to cover some nice results such as the Borel-Weil-Bott theorem. Towards this end we begin the term with a crash-course in algebraic groups.