Kostant partition functions for affine Kac-Moody algebras

Abstract

Employing the method of generating functions in conjunction with various number-thoretic identities, we obtain recursion relations for the Kostant partition functions for the affine Kac-Moody algebras The partition functions for the higher rank algebras are expressed in terms of SUˆ(2) partition functions. We derive certain number-theoretic identities using the equivalence of our result with the expressions derived by Kac and Peterson.

Keywords

• affine Kac-Moody algebras
• Kostant partition functions
• weight-multiplicities
• positive and simple roots
• diophantine equations
• Weyl group
• Euler identity
• Jacobi's triple and quintuple product identities
• Tannery-Molk identity.