{"id":"hexagon/2610.00733","pdf":"https://hexagonmath.org/pdf/2610.00733v1","url":"https://hexagonmath.org/abs/2610.00733v1","tags":["msc:17B69","msc:18M20","msc:11E12","msc:11F03","msc:81T40","Drinfeld center","Haagerup fusion category","Heisenberg commutant","genus of vertex operator algebras","lattice"],"score":0,"title":"Haagerup vertex operator algebras at central charge eight","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Cédric ARHANCET"],"reviews":0,"subject":"math.QA","summary":"Evans and Gannon showed that a positive vertex operator algebra of central charge eight whose representation category is the Drinfeld center $Z(\\cal H_3)$ of the Haagerup fusion category has one of two character vectors, with six or nineteen currents. Call such an algebra, if strongly rational, a Haagerup algebra. We prove that a Haagerup algebra $U$ has six currents, that $U_1 \\cong \\mathfrak{sl}_2 \\oplus \\mathfrak{sl}_2$ embeds into $V_{E_6 \\oplus A_2}$ in one of two explicit ways, with levels $(1,39)$ or $(3,13)$, and we determine the lowest weight spaces of its modules and $U_2$ as…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}