Resumen de Coxeter quiver representations in fusion categories and Gabriel’s theorem
Edmund Heng
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.
