Data
- Title: Generalized diagram categories and monoids, and their representations
- Authors: Matthias Fresacher, Willow Stewart and Daniel Tubbenhauer
- Status: preprint. Last update: Fri, 19 Dec 2025 02:32:14 UTC
- ArXiv link: https://arxiv.org/abs/2512.17177
Abstract
Classical diagram categories and monoids, including the Temperley–Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of diagram categories and monoids. In this paper we introduce this family and develop a unified approach to their representation theory.
A few extra words
For example, in large generality their representations behave like a Gaussian, e.g. for Temperley–Lieb:
