{"id":"hexagon/2610.00490","pdf":"https://hexagonmath.org/pdf/2610.00490v1","url":"https://hexagonmath.org/abs/2610.00490v1","tags":["msc:17B69","msc:18M20"],"score":0,"title":"Vertex Operator Algebra Realizations of Twisted Haagerup–Izumi Doubles","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Andrew Riesen","David E. Evans"],"reviews":0,"subject":"math.QA","summary":"We construct vertex operator algebras realizing an infinite family of twisted, nonunitary Haagerup--Izumi doubles. For every odd integer $N\\geq 3$, we construct a spherical fusion category $\\mathcal{F}_N$ with the Haagerup--Izumi fusion rules for $\\mathbb{Z}/N\\mathbb{Z}$ and pointed associator of exact order $N$, and realize its Drinfeld center as the ribbon category of modules of an explicit vertex operator algebra $\\mathscr{V}_N$. The construction begins with a uniform family of strongly rational Virasoro extensions, whose irreducible modules and theta-function characters we determine. A…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}