Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra

• 成果类型: Article
• 署名作者: Moeller, Sven; Scheithauer, Nils R.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.197.1.4
• 发表日期: 2023
• 页码: 221-288
• 关键词: central charge 24; one lie-algebra; automorphic products; monstrous moonshine; modular-invariance; CLASSIFICATION; constructions; uniqueness; orbifolds

摘要

We prove a dimension formula for the weight-1 subspace of a vertex operator algebra Vorb(g) obtained by orbifolding a strongly rational, holo-morphic vertex operator algebra V of central charge 24 with a finite-order automorphism g. Based on an upper bound derived from this formula we introduce the notion of a generalised deep hole in Aut(V ).Then we show that the orbifold construction defines a bijection between the generalised deep holes of the Leech lattice vertex operator algebra V Lambda with non-trivial fixed-point Lie subalgebra and the strongly rational, holo-morphic vertex operator algebras of central charge 24 with non-vanishing weight-1 space. This provides a uniform construction of these vertex opera-tor algebras and naturally generalises the correspondence between the deep holes of the Leech lattice Lambda and the 23 Niemeier lattices with non-vanishing root system found by Conway, Parker, Sloane and Borcherds.