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Braidings for Quantum Groups at Roots of 1

Algebra & Discrete Mathematics

Speaker: Noah Snyder, UC-Berkeley
Location: 1147 MSB
Start time: Thu, Feb 22 2007, 3:10PM

One of the main reasons for interests in quantum groups is the existence of a nontrivial braiding $R: V\otimes W \rightarrow W \otimes V$ for representation at generic $q$. This braiding is what gives applications of Quantum Groups to knot theory. When $q$ is a root of $1$ (in the Kac-DeConcini specialization), a traditional braiding does not exist. However, the notion can be modified and extended. I'll be talking about the work of Kashaev and Reshetikhin for $sl_2$ and current work of Reshetikhin and mine extending that to arbitrary type. I'll also discuss briefly potential applications to knot theory.