Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras

Abstract

We show that the Inönü-Wigner contraction naturally associated to a reduction chain s ⊃ s′ of semisimple Lie algebras induces a decomposition of the Casimir operators into homogeneous polynomials, the terms of which can be used to obtain additional mutually commuting missing label operators for this reduction. The adjunction of these scalars that are no more invariants of the contraction allow to solve the missing label problem for those reductions where the contraction provides an insuflcient number of labelling operators.