Recursion relations and branching rules for simple Lie algebras

Details Recursion relations and branching rules for simple Lie algebras Recursion relations and branching rules for simple Lie algebras

1995-05-04

arxiv.org/abs/q-alg/9505006v1

Mathematics

Quantum Algebra

15p.,LaTex

Scientific paper

10.1088/0305-4470/29/5/020

The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights $\Gamma$ specific for each injection. The structure of $\Gamma$ is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for $A_{3} \oplus u(1) \to B_{4}$ injection.

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