Coxeter quiver representations in fusion categories and Gabriel’s theorem

Edmund Heng

Ayuda

Coxeter quiver representations in fusion categories and Gabriel’s theorem

Edmund Heng ^[1]
1. [1] Institut des Hautes Études Scientifiques
  
  Institut des Hautes Études Scientifiques
  
  Arrondissement de Palaiseau, Francia
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-42
Idioma: inglés
DOI: 10.1007/s00029-024-00947-1
Enlaces
- Texto completo
Resumen
- We introduce a notion of representation for a class of generalised quivers known as Coxeter quivers. These representations are built using fusion categories associated to Uq (sl2) at roots of unity and we show that many of the classical results on representations of quivers can be generalised to this setting. Namely, we prove a generalised Gabriel’s theorem for Coxeter quivers that encompasses all Coxeter–Dynkin diagrams—including the non-crystallographic types H and I. Moreover, a similar relation between reflection functors and Coxeter theory is used to show that the indecomposable representations correspond bijectively to the (extended) positive roots of Coxeter root systems over fusion rings.
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