Generalized diagram categories and monoids, and their representations
A unified family of diagram categories and monoids, built from cobordism-style pictures with extra twists.
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: 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.
What is the point?
Many diagram algebras look different on the surface, but they are variants of the same basic idea: compose pictures and study the resulting algebra. This paper enlarges the menu of possible pictures and then asks how their representations behave.
many classical diagram categories at once.
new diagrammatic ingredients.
large families show Gaussian-type behaviour.
A picture
In large generality, the representation theory shows familiar asymptotic shapes.
