Georgia Institute of Technology College of Sciences

The colored Jones polynomial is a quantum knot invariant which can be constructed as a Reshetikhin–Turaev invariant using representations of $U_q(sl_2)$. Khovanov homology categorifies the Jones polynomial and by extension categorifies the representation theory of $sl_2$. Of particular interest is sutured annular Khovanov homology, which admits a structure as an $sl_2$-module. We will discuss a result of Grigsby–Licata–Wehrli that this structure is a representation-theoretic invariant of an annular link. Time permitting, we will discuss some of the structure of this representation, and extend the result to $sl_n$.