Webs for quantum orthogonal groupAlgebra & Discrete Mathematics
|Haihan Wu, UC Davis
|Mon, Mar 13 2023, 4:10PM
The Jones polynomial can be defined with the Temperley-Lieb category, whose Karoubian completion is equivalent to the representation category of quantum sl(2). When we generalize the sl(2) case to the sl(n) case, the functor from the HOMFLY category to the representation category has a kernel. In order to find a graphical category which is equivalent to the representation category, one can introduce trivalent vertices and define a Spider (also know as a web category). When we look at the generalization from type A to type B,C,D, the functor from the BMW category to the representation category also has a kernel. However, we can define a web category which is equivalent to the representation category of quantum orthogonal group. This talk is based on an upcoming joint work with Elijah Bodish.