Data

• Title: Affine diagram categories, algebras and monoids
• Authors: David He and Daniel Tubbenhauer
• Status: preprint. Last update: Fri, 5 Dec 2025 08:11:40 UTC
• Code and (possibly empty) Erratum: Click
• ArXiv link: https://arxiv.org/abs/2512.05510

Abstract

We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley–Lieb, partition, Brauer, Motzkin, rook Brauer, rook, and planar rook algebras. We give generators and relation presentation for them and their associated categories, study their representation theory, and the asymptotic behavior of tensor products of their representations in the monoid case.

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