Quantum representations of braids

Geometry Topology Student Seminar
Wednesday, March 25, 2015 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
Solutions to the Yang-Baxter equation are one source of representations of the braid group. Solutions are difficult to find in general, but one systematic method to find some of them is via the theory of quantum groups. In this talk, we will introduce the Yang-Baxter equation, braided bialgebras, and the quantum group U_q(sl_2). Then we will see how to obtain the Burau and Lawrence-Krammer representations of the braid group as summands of natural representations of U_q(sl_2).