# 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…

## 15 Citations

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We associate with a generalised deep hole of the Leech lattice vertex operator algebra a generalised hole diagram. We show that this Dynkin diagram determines the generalised deep hole up to…