Campoamor Stursberg, Otto-Rudwig2023-06-202023-06-2020071751-811310.1088/1751-8113/40/49/011https://hdl.handle.net/20.500.14352/50621We analyze under which conditions the missing label problem associated to a reduction chain s′ ⊂ s of (simple) Lie algebras can be completely solved by means of an In¨on¨u-Wigner contraction g naturally related to the embedding. This provides a new interpretation of the missing label operators in terms of the Casimir operators of the contracted algebra, and shows that the available labeling operators are not completely equivalent. Further, the procedure is used to obtain upper bounds for the number of invariants of affine Lie algebras arising as contractions of semisimple algebras.engjournal articlehttps//doi.org/10.1088/1751-8113/40/49/011http://iopscience.iop.org/1751-8121/40/49/011/open access512.554.3Lie groupIrreducible representationMultipletsSubgroup embeddingLabelling operatorsWigner supermultiplet modelMissing label problemCasimir operatorsContracted algebraInönü-Wigner contractionÁlgebra1201 Álgebra