Branching rules of sp(6) ↓ sp(4) × sp(2) and bases of eigenstates

Abstract

An explicit formula describing the branching of representations of sp(6) according to the reduction chain sp(6) ↓ sp(4) × sp(2) is given. This allows to classify the multiplicity free reductions and, moreover, obtain the multiplicity for each sp(4) × sp(2) representation. We compare the method with the approach based on the theory of S-functions, pointing out the strengths and weaknesses of the explicit formula. The branching rule is used to construct an orthogonal basis of eigenstates for sp(6), where degenerations are solved using a scalar instead of the standard missing label operator.