# Web Categories

## GAP (Geometry, Algebra, Physics) Seminar

## Meeting Details

For more information about this meeting, contact Donna Cepullio, Ping Xu, Mathieu Stiénon.

**Speaker:** Peter Debello, Penn State

**Abstract:** In https://arxiv.org/abs/q-alg/9712003, Kuperberg defines so-called "spiders" for $A_2, B_2$ and $G_2$, generalizing a classical construction of Rumer-Teller-Weyl for $\mathfrak{sl}_2(\mathbb{C})$. These spiders yield a diagrammatic generators and relations description for the monoidal category $\mathbf{Rep}(\mathfrak{g})$ of finite-dimensional complex linear representations of $\mathfrak{g}$. In these diagrammatic categories, hom-spaces consist of braid-like diagrams: so, such categories have come to be called "web" categories.
I'll discuss some examples of web categories, mainly focusing on the Temperley-Lieb category $\mathcal{TL}(-2)$ and the partition category. I'll also discuss open problems we are working on such as constructing webs for the finite group $SL_2(\mathbb{F}_q)$ (joint with Daniel Tubbenhauer).

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 11/15/2022

**Time:** 2:30pm - 3:30pm