Generalized diagram categories and monoids, and their representations

2025/12/19 by Fresacher, Matthias, Stewart, Willow, Tubbenhauer, Daniel
#05E10 #05E16 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Primary: 20G05 #Representation Theory (math.RT) #Secondary: 20M30

paper · doi:10.48550/arxiv.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.

Citations

• Affine diagram categories, algebras and monoids
• Representations of Cyclic Diagram Monoids
• Growth Problems of Quantum Groups
• Representation Gap of the Motzkin Monoid
• Twisted products of monoids
• Quantum topology without topology
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• Uncoiled affine Temperley-Lieb algebras and their Wenzl-Jones projectors
• Super invariant theory in positive characteristic
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• Integral Schur-Weyl duality for partition algebras
• Simple Modules for Temperley-Lieb Algebras and related Algebras
• Jellyfish partition categories
• Simple modules for the partition algebra and monotone convergence of Kronecker coefficients
• The first fundamental theorem of invariant theory for the orthosymplectic supergroup
• On geometrically defined extensions of the Temperley-Lieb category in the Brauer category
• Motzkin Algebras
• On the irreducible representations of a finite semigroup
• Convergence rates of random walk on irreducible representations of finite groups
• Partition Algebras
• Generalized Temperley-Lieb algebras and decorated tangles
• The blob algebra and the periodic Temperley-Lieb algebra

Related

• Affine diagram categories, algebras and monoids
• Set-partition tableaux and representations of diagram algebras
• Polar Brauer categories, infinitesimal braids and Lie superalgebra representations
• Diagram categories of Brauer type
• Transformation representations of diagram monoids