Coxeter planes as fixed points of Verlinde fusion rings

TL;DR

This paper constructs Coxeter planes for ADE Coxeter groups as fixed points under hypergroup actions derived from Verlinde fusion rings, linking geometric and algebraic structures.

Contribution

It introduces a novel construction of Coxeter planes as fixed points of hypergroup actions related to Verlinde fusion rings for ADE groups.

Findings

Coxeter planes identified as fixed points of hypergroup actions

Links between Coxeter groups, hypergroups, and fusion rings established

Provides a new geometric interpretation of ADE classification

Abstract

For the Coxeter groups of ADE type, we provide a construction of their Coxeter planes as fixed points of actions of hypergroups associated to Verlinde fusion rings. This builds upon the well-known ADE classification of $\mathbb{Z}_+$-modules over these fusion rings.