{"id":"hexagon/2610.00508","pdf":"https://hexagonmath.org/pdf/2610.00508v1","url":"https://hexagonmath.org/abs/2610.00508v1","tags":["msc:17B69","msc:18M20"],"score":0,"title":"Vertex operator algebra realizations of untwisted Haagerup--Izumi centers","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Andrew Riesen","David E. Evans"],"reviews":0,"subject":"math.QA","summary":"For every odd integer $N\\geq3$, we construct an untwisted Haagerup--Izumi fusion category $\\mathcal H_N$ on the negative spherical branch and a simple, self-contragredient, regular, $C_2$-cofinite vertex operator algebra $E_N$ of central charge $-16N$, together with an equivalence of modular fusion categories: \\[ \\operatorname{Rep}(E_N)\\simeq Z(\\mathcal H_N). \\] The VOA $E_N$ is rational, has exactly $N^2+3$ irreducible modules, and is lower bounded and integer graded, with least conformal degree $-(N-1)/2$. The proof begins with a CFT-type cyclic Virasoro extension of central charge $-5N$,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}