Title: Induced Representations of $U_q(\mathfrak{sl_2})$ and $U_q(\mathfrak{sl_3})$, and the Alexander Polynomial
Speaker: Matthew Harper (Ohio State University)
Abstract: The Alexander polynomial arises by considering the knot invariant presented by Ohtsuki using a family of representations of $U_q(\mathfrak{sl_2})$ at a root of unity. The multi-variable Alexander polynomial is a generalization of the Alexander polynomial to links where each strand is colored by a representation in a different parameter. In this talk, we will review the multi-variable construction and build the analogous $U_q(\mathfrak{sl_3})$ representations from Verma modules. After noting some properties of these representations, we will explore their tensor product structure. More specifically, we provide the fusion rules for decomposable tensor products and discuss consequences of this decomposition.
Seminar URL: http://yutsumura.com/quantum-algebra-topology-seminar/
