Hi all, I've just finished a graduated course on KacMoody algebras, and I'm really looking for some reading in regard to their applications to Quantum Mechanics. Can you help?

I can recommend the article of Louise Dolan, "The Beacon of Kac Moody Symmetry for Physics", and the references given therein. From the summary: In addition to (this) wide application to physical theories, the KacMoody algebras are also relevant to number theory and modular forms. The link is http://www.ams.org/notices/199512/dolan.pdf. 


I highly recommend the book "Affine Lie Algebras, Weight Multiplicities, and Branching Rules": a very pleasant reading, both for its math and for its physics content. 

