International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 539-552
doi:10.1155/S0161171297000732
Kostant partition functions for affine Kac-Moody algebras
T.S. Santhanam1
and R. Chakrabarti2
1Department of Science and Mathematics, Parks College of Saint Louis University, Cahokia 62206, Illinois, USA
2Department of Theoretical Physics, University of Madras, Madras 600025, India
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.