Title

Vertex operator algebras for type G affine Lie algebras

Date of Completion

January 2009

Keywords

Physics, Quantum|Theoretical Mathematics

Degree

Ph.D.

Abstract

We consider admissible modules for Kac-Moody Lie algebras from the point of view of Vertex Operator Algebras (VOA). The admissible representations of affine Lie algebras are modular invariant representations, and were first studied by Kac and Wakimoto as generalizations of integrable modules. We consider VOA associated to admissible representations of type G affine Lie algebras at admissible third-integer levels. The VOA corresponding to these represenations are not rational, but we show that there are only finitely many irreducible weak-modules in a certain category of modules, for three different admissible levels. This confirms part of a general conjecture given by Adamovic and Milas for all VOA corresponding to admissible representations. ^