Tubular partitions and representations of the quantum automorphism group of a homogeneous rooted tree

2025/09/26 by Brownlowe, Nathan, Robertson, David
#FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2509.22201

Abstract

We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a homogeneous rooted tree.

Citations

• Self-similar quantum groups
• Almost all trees have quantum symmetry
• Nonlocal Games and Quantum Permutation Groups
• Free wreath product quantum groups : the monoidal category, approximation properties and free probability
• The full classification of orthogonal easy quantum groups
• The combinatorics of an algebraic class of easy quantum groups
• Easy quantum groups and quantum subgroups of a semi-direct product quantum group
• On the classification of easy quantum groups
• Quantum automorphism groups of finite graphs

Related

• Patterns in trees and quantum automorphism groups
• Quantum automorphism groups of trees
• Representation theory of the group of automorphisms of a finite rooted tree
• Autoequivalences of tensor categories attached to quantum groups at roots of 1
• Quantum Groups at Roots of Unity and Modularity