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

@article{Mller2019DimensionFA,
  title={Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra},
  author={Sven Karup M{\o}ller and Nils R. Scheithauer},
  journal={Annals of Mathematics},
  year={2019}
}
We prove a dimension formula for the weight-1 subspace of a vertex operator algebra $V^{\operatorname{orb}(g)}$ obtained by orbifolding a strongly rational, holomorphic 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 $\operatorname{Aut}(V)$. We then give a construction of all 70 strongly rational, holomorphic vertex operator algebras of central charge… 

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