Title: Isomorphisms between quantum groups and classical algebras
Speaker: Sachin Gautam, OSU
Abstract: Quantum groups are certain Hopf algebras associated to a simple Lie algebra, discovered by Drinfeld and Jimbo around 1985. It was also observed by Drinfeld that, as algebras, these quantum groups are isomorphic to their classical analogues. The existence of such algebra isomorphisms is a consequence of rather deep cohomological arguments, which makes the problem of finding an explicit one both non-trivial and interesting.
In this talk, I will present a family of such isomorphisms for the Lie algebra gl(n), and some natural related questions. I will also discuss the relation this problem bears with classical invariant theory, Poisson geometry and Stokes' phenomenon. This talk is based on my recent joint work with A. Appel.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Henri Moscovici.
