Quantum Topology / Hopf Algebra Seminar
Sachin Gautam
Columbia University, NY
Yangians, quantum loop algebras and elliptic quantum groups
Abstract: This talk will focus on three affine quantum groups associated
to a simple Lie algebra, namely the Yangian, quantum loop algebra and
elliptic quantum group. These correspond respectively to rational,
trigonometric and elliptic solutions
of the Yang--Baxter equation, and arise in their simplest guises as
symmetries of Heisenberg XXX, XXZ and XYZ lattice models. In previous
work, we showed how to construct representations of the quantum loop
algebra from those of the Yangian, and vice versa, thus settling the long
standing problem of relating their representations. I will explain
this construction and its extension to the case of elliptic quantum
groups. This talk is based on a joint work with V. Toledano Laredo.
Thursday December 4, 2014 at 4:00 PM in SEO 612