Zones of uniform decomposition in tensor products

Abstract

Let V λ {V_\lambda } be a finite dimensional irreducible module for a complex semisimple Lie algebra. It is shown that the decomposition of tensor products V λ ⊗ V τ {V_\lambda } \otimes {V_\tau } for all dominant integral weights τ \tau may be derived from those for a finite set of such τ \tau . An explicit choice of such a finite set (depending on λ \lambda ) is given.