Internal labelling operators and contractions of Lie algebras

Details Internal labelling operators and contractions of Lie algebras Internal labelling operators and contractions of Lie algebras

2007-06-18

arxiv.org/abs/0706.2581v1

J.Phys.A40:14773-14790,2007

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 2 tables

Scientific paper

10.1088/1751-8113/40/49/011

We analyze under which conditions the missing label problem associated to a reduction chain $\frak{s}^{\prime}\subset \frak{s}$ of (simple) Lie algebras can be completely solved by means of an In\"on\"u-Wigner contraction $\frak{g}$ 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.

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