MS Seminar (Mathematics - String Theory)

Speaker: Andrea Appel (U of Edinburgh)
Title: Dual exponentials and their quantization
Date: Tue, Dec 11, 2018, 15:30 - 17:00
Place: Seminar Room A
Abstract: The linearization theorem of Ginzburg and Weinstein states that, for any compact Lie group with its standard Poisson structure, there exists a dual exponential, that is, a Poisson diffeomorphism between the dual Poisson Lie group and the dual Lie algebra with the Kirillov Poisson structure.This was later generalized by Boalch, through an irregular Riemann-Hilbert correspondence, and by Enriquez-Etingof-Marshall, relying on Etingof-Kazhdan quantization of Lie bialgebras.
In this talk, I will show how, as initially conjectured by Ginzburg and Weinstein, examples of dual exponentials in type A can be obtained as semiclassical limit of certain explicit algebra isomorphisms between the quantum group of sl(n) and the universal enveloping algebra. This is joint work with S. Gautam.
Remarks: Blackboard talk