Representations of Coxeter groups over fusion rings and hyperplane complements

2025/11/06 by Edmund Heng, Luis Paris, Heng, Edmund +1
Mathematics · #18M20 #20F36 #20F55 #52C35 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2511.04836

openalex publication_date 2025/11/06 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

We study faithful realisations of Coxeter groups over fusion rings and study Vinberg systems associated to them. We show that they induce embeddings of hyperplane complements, which provide geometrical realisations of certain types of strong admissible (LCM) homomorphisms between Artin--Tits groups.

Citations

• Stability conditions and Artin--Tits groups
• Classification of finite type fusion quivers
• Coxeter embeddings are injective
• Coxeter quiver representations in fusion categories and Gabriel's theorem
• Artin monoids inject in their groups

Related

• Coxeter quiver representations in fusion categories and Gabriel's theorem
• Semisimple Zariski closure of Coxeter groups
• Hyperplane arrangements associated to symplectic quotient singularities
• Generalisations of the Tits representation
• On convex hulls of orbits of Coxeter groups and Weyl groups