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An order-five Haagerup--Izumi vertex operator algebra at central charge eight

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.OA — Operator Algebrasmath-ph — Mathematical Physics

Contributed by Tzu Chen Huang ↗

Version 1 / Oct 13, 2026 / CC BY 4.0

Abstract

We construct an explicit unitary strongly rational vertex operator algebra UU of central charge eight inside VA4⊕A4V_{A_4\oplus A_4} and identify Rep(U)Rep(U) with the Drinfeld center of the positive order-five Haagerup--Izumi category. The construction adjoins one algebraic weight-two field to a diagonal affine sl2\mathfrak{sl}_2 at level forty and the ambient conformal vector. Exact finite lattice identities imply strong generation and C2C_2-cofiniteness. A finite integral order in the actual Zhu algebra descends semisimplicity from a 15901590-dimensional upper presentation over F10069\mathbb F_{10069}. To determine the modules, we combine the good-prime block bound with lattice character growth and a Wronskian inequality. The resulting full branching has an irreducible congruence complement of dimension at most fifteen; its exact classification forces all fourteen denominator-2929 sectors. Finally, the actual holomorphic E8E_8 extension determines the boundary fusion category and its associator. The proof is computer-assisted, with exact arithmetic certificates separated from exploratory numerical evidence.

Provenance statement

AI systems assisted with exploration, calculations, proof development, and writing. The work uses saved exact-arithmetic certificates and written mathematical reductions.

Tools used

NumPy developers
NumPyVersion 2.4.6
SymPy development team
SymPyVersion 1.14.0
Alex Martelli, Case Van Horsen and contributors
gmpy2Version 2.3.1
FLINT development team
FLINTVersion 3.4.0
GNU GMP developers
GMPVersion 6.3.0
The GAP Group
GAPVersion 4.16.1
Siu-Hung Ng, Yilong Wang, Samuel Wilson
SL2RepsVersion 1.1
SciPy developers
SciPyVersion 1.16.2
Fredrik Johansson and contributors
mpmathVersion 1.4.1

References

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Version history

  1. v1Submitted by Tzu Chen HuangInitial depositCurrentOct 13, 2026