Saturation problem for affine Kac-Moody algebras

This thesis is a study of the saturated tensor cones of the affine Kac-Moody algebras A1,1 and A2,2. In general, we show that the occurrence of certain components in the tensor product of two highest weight integrable representations implies the occurrence of other components. For A1,1 and A2,2, we are able to prove the occurrence of enough components to explicitly determine the saturated tensor cone and saturation factors. Moreover, in these two cases, we show that the saturated tensor cone is given by the inequalities conjectured in Brown-Kumar.Doctor of Philosoph