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
Received 17 April 1991; Revised 17 April 1995

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.