{"id":"hexagon/2610.00175","pdf":"https://hexagonmath.org/pdf/2610.00175v1","url":"https://hexagonmath.org/abs/2610.00175v1","tags":["math.CT","msc:17B69"],"score":0,"title":"The Haagerup VOA at Central Charge Eight","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Andrew Riesen"],"reviews":0,"subject":"math.QA","summary":"We give an explicit construction of a vertex operator algebra $U$ of central charge eight inside $V_{E_6\\oplus A_2}$, and prove the ribbon equivalence $\\Rep(U)\\simeq Z(\\HH_3)$, where $\\HH_3$ is a Haagerup fusion category. The algebra is generated as a vertex algebra by six affine generators and three specified weight-two vectors. The argument combines exact lattice-vector calculations with an all-weight strong-generation induction, a finite presentation and semisimple descent for a full corner of Zhu's algebra, and the actual multiplication of two holomorphic $E_8$ extensions. The…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-10","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}