BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar BIMSA-Tsinghua Quantum Symmetry Seminar Classification of Composites of Fibonacci Fusion Categories: Coxeter Rigidity, Construction, and Uniqueness
Classification of Composites of Fibonacci Fusion Categories: Coxeter Rigidity, Construction, and Uniqueness
Organizers
Quan Chen , Linzhe Huang , Zhengwei Liu , Shuang Ming , Sebastien Palcoux , Yilong Wang , Jinsong Wu
Speaker
Huixuan He
Time
Wednesday, November 18, 2026 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
The Fibonacci fusion category is one of the simplest nontrivial fusion categories, generated by a simple object $X$ satisfying the fusion rule $X^2=1+X$. In this talk, I will discuss the classification of semisimple tensor categories generated by finitely many Fibonacci objects, allowing the resulting categories to have infinitely many simple objects. We show that their fusion rules are described by Coxeter–Hecke rings, with Coxeter exponents restricted to $2$, $3$, or $\infty$. In particular, the finite-rank cases correspond precisely to Coxeter systems of ADE type. For every such system, we explicitly construct the corresponding fusion category and establish its uniqueness up to marked tensor equivalence. I will outline the ideas behind the rigidity and construction results, and explain how the Davis complex is used in the uniqueness proof to control coherence constraints and gauge transformations.