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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References

SHOWING 1-10 OF 93 REFERENCES

A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications

In this thesis we develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic vertex operator algebra V. To this end we describe the fusion algebra of the…

Meromorphic c = 24 Conformal Field Theories

. Modular invariant conformal field theories with just one primary field and central charge c = 24 are considered. It has been shown previously that if the chiral algebra of such a theory contains…

On the Genus of the Moonshine Module

We provide a novel and simple description of Schellekens’ seventy-one affine KacMoody structures of self-dual vertex operator algebras of central charge 24 by utilizing cyclic subgroups of the glue…

Reine Angew

  • Math., 759:61–99,
  • 2020

The Weil representation of SL2(Z) and some applications

The theta function of a positive definite even lattice of even rank generates a representation of SL2(Z) on the group algebra of the discriminant form of the lattice. This representation goes back to…

Hecke operators on Γ0(m)

Schellekens' list and the very strange formula

C 2 -Cofiniteness of Cyclic-Orbifold Models

: We prove an orbifold conjecture for conformal field theory with a solvable automorphism group. Namely, we show that if V is a C 2 -cofinite simple vertex operator algebra and G is a finite solvable…

APPLICATION OF A Z3-ORBIFOLD CONSTRUCTION TO THE LATTICE VERTEX OPERATOR ALGEBRAS ASSOCIATED TO NIEMEIER LATTICES

By applying Miyamoto’s Z3-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices and their automorphisms of order 3, we construct holomorphic vertex operator…

A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24

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…
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