Branching index sum rules for simple Lie algebras

Abstract

Let L and L0 be a simple Lie algebra and its sub-Lie algebra, respectively. Then, a given irreducible representation ω of L decomposes into a direct sum of irreducible components of L0, which is called the branching rule. The general Dynkin indices introduced earlier satisfy many sum rules for the branching rule. These are found to be strong enough to uniquely determine the branching rule for many cases we have studied. The sum rules are especially useful for cases of exceptional Lie algebras.