Kac-Moody and Virasoro algebras

Understand

These are the notes for a Part III course given in the University of Cambridge in autumn 1998.

• They contain an exposition of the representation theory of the Lie algebras of compact matrix groups, affine Kac-Moody algebras and the Virasoro algebra from a unitary point of view.
• The treatment uses many of the methods of conformal field theory, in particular the Goddard-Kent-Olive construction and the Kazami-Suzuki supercharge operator, a generalisation of the Dirac operator.
• The proof of the Weyl character formula is taken from unpublished notes of Peter Goddard.