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Kostant partition functions for affine Kac-Moody algebras

Author(s): T. S. Santhanam | R. Chakrabarti

Journal: International Journal of Mathematics and Mathematical Sciences
ISSN 0161-1712

Volume: 20;
Issue: 3;
Start page: 539;
Date: 1997;
Original page

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.

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.
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