We will give a lattice-theoretical interpretation of generalized deep holes of the Leech lattice VOA VΛ. 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 V1 and the set of equivalence classes of pairs (𝜏,β̃ ) satisfying certain conditions, where 𝜏∈Co0 and β̃ is a 𝜏-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.
This video was produced by CIRM as part of the conference Vertex algebras and representation theory.
