Quantum G2 at roots of unity: diagrams vs. algebra

Date & time

3.30–4.30pm 20 March 2018


John Dedman Building 27, Room G35.


Noah Snyder (Indiana)


 Scott Morrison

For generic $q$, Kuperberg's $G_2$ spider agrees with the category of representations of the quantum group.  What happens when $q$ is a root of unity?  Except for a few small roots of unity, it turns out that the spider agrees with the category of tilting modules for $G_2$, and as a consequence the semisimplified spider agrees with the semisimple quantum group fusion category.  As a corollary of this result together with the trivalent categories classification, we can prove a Kazhdan-Wenzl-style recognition theorem for $G_2$.  This is joint work with Victor Ostrik.

Updated:  21 March 2018/Responsible Officer:  Director/Page Contact:  School Manager