Abstract
In this project, it is proposed to work on the following problems. 1. To prove a conjecture of polynomial behavior of root multiplicities for the Kac-Moody algebras HA_n^(1), HC_n^(1), and HD_n^(1). 2. To investigate the decomposition of the tensor product of two arbitrary integrable highest weight modules for affine Lie algebras. 3. To investigate the scattering behavior of soliton c…