Physics – Mathematical Physics
Scientific paper
2008-10-25
J. Phys. Conf. Ser. 128 (2008) 012052
Physics
Mathematical Physics
Scientific paper
10.1088/1742-6596/128/1/012052
We show that the In\"on\"u-Wigner contraction naturally associated to a reduction chain $\frak{s}\supset \frak{s}^{\prime}$ 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 insufficient number of labelling operators.
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