Apparaît dans la collection : Vertex Algebras and Representation Theory / Algèbres vertex et théorie des représentations
We will give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA $V_\Lambda$. We show that a generalized deep hole defines a 'true' automorphism invariant deep hole of the Leech lattice. We will also discuss a correspondence between the set of isomorphism classes of holomorphic VOA $V$ of central charge $24$ having non-abelian $V_1$ and the set of equivalence classes of pairs $(\tau, \tilde{\beta})$ satisfying certain conditions, where $\tau\in Co_0$ and $\tilde{\beta}$ is a $\tau$-invariant deep hole of squared length $2$. It provides a new combinatorial approach towards the classification of holomorphic VOAs of central charge $24$. Finally, we will discuss an observation of G.Höhn, which relates the weight one Lie algebra of holomorphic VOAs of central charge $24$ to certain codewords associated with the glue codes of Niemeier lattices.
De Dimitry Gurevich
De Jorgen Ellegaard Andersen
De Olivier Benoist
De Viviane Pons
