RECURSION-RELATIONS AND BRANCHING-RULES FOR SIMPLE LIE, ALGEBRAS

The branching rules between simple Lie algebras and their regular (max imal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is pr oved to be the factorized version of the other. The factorization prop erty is based on the existence of the set of weights Gamma specific fo r each injection. The structure of Gamma is easily deduced from the co rrespondence between the root systems of the algebra and subalgebra. T he recursion relations thus obtained give rise to a simple and effecti ve algorithm for branching rules. The details are illustrated by perfo rming the explicit decomposition procedure for the injection A(3) circ le plus u(1) --> B-4.