RT Journal Article T1 Internal labelling problem: an algorithmic procedure A1 Campoamor Stursberg, Otto Ruttwig AB Combining the decomposition of Casimir operators induced by the embedding of a subalgebra into a semisimple Lie algebra with the properties of commutators of subgroup scalars, an analytical algorithm for the computation of missing label operators with the commutativity requirement is proposed.Two new criteria for subgroups scalars to commute are given. The algorithm is completed with a recursive method to construct orthonormal bases of states. As examples to illustrate the procedure, four labelling problems are explicitlystudied. PB IOP Science SN 1751-8113 YR 2011 FD 2011 LK https://hdl.handle.net/20.500.14352/43754 UL https://hdl.handle.net/20.500.14352/43754 LA eng NO Elliott J P 1958 Proc. R. Soc. A 245 128, 562Jarvis P D 1974 J. Phys. A: Math. Nucl. Gen. 7 1807Rowe D J 1994 J. Math. Phys. 35 3178Hecht K T 1994 J. Phys. A: Math. Gen. 27 3445Rowe D J 1995 J. Math. Phys. 36 1520Sharp R T and Pieper S C 1968 J. Math. Phys. 9 663Sharp R T 1970 Proc. Camb. Phil. Soc. 68 571Sharp R T 1975 J. Math. Phys. 16 2050Gaskell R, Rosensteel G and Sharp R T 1981 J. Math. Phys. 22 2732Jarvis P D 1979 J. Phys. A: Math. Gen. 12 1Jarvis P D and Zhang R B 2005 J. Phys. A: Math. Gen. 38 L219Boya L J and Campoamor-Stursberg R 2009 J. Phys. A: Math. Theor. 42 205235Campoamor-Stursberg R 2008 J. Phys. Conf. Ser. 128 012052Campoamor-Stursberg R 2008 arXiv:0805.2981 [hep-th]Van der Jeugt 1984 J. Math. Phys. 25 1221Bincer A M 1983 J. Math. Phys. 24 1695Peccia A and Sharp R T 1976 J. Math. Phys. 17 1313Pecina Cruz J N 1994 J. Math. Phys. 35 3146Campoamor-Stursberg R 2007 J. Phys. A: Math. Theor. 40 14773Judd B R, Miller W, Patera J and Winternitz P 1974 J. Math. Phys. 15 1787Berezin F A 1967 Funkt. Anal. Prilozh. 1 1Iachello F 2006 Lie Algebras and Applications (New York: Springer)Pan F, Cao Y-F and Pan Z-Y 1989 J. Phys. A: Math. Gen. 22 4105Bincer A M and Riesselmann K 1993 J. Math. Phys. 34 5935Campoamor-Stursberg R 2005 J. Phys. A: Math. Gen. 38 4187Racah G 1951 Group Theory and Spectroscopy (Princeton, NJ: Princeton University Press)Gel’fand I M 1950 Mat. Sb. 26 112De Meyer H, Vanden Berghe G, Van der Jeugt J and De Wilde P 1985 J. Math. Phys. 26 2124De Baerdemacker S, Heyde K and Hellemans V 2007 J. Phys. A: Math. Theor. 40 2733Campoamor-Stursberg R 2009 J. Phys. Conf. Ser. 175 012008Giroux Y and Sharp R T 1987 J. Math. Phys. 28 1671Couture M and Sharp R T 1989 J. Phys. A: Math. Gen. 22 1525Wybourne B G and Bowick M J 1977 Aust. J. Phys. 30 259Slansky R 1981 Phys. Rep. 79 1Wybourne B G 1995 Lithuanian J. Phys. 35 123Keurentjes A 2003 Nucl. Phys. B 658 303Boyko V, Patera J and Popovych R 2006 J. Phys. A: Math. Gen. 39 5749Boyko V, Patera J and Popovych R 2007 J. Phys. A: Math. Theor. 40 113 NO UCM-BSCH DS Docta Complutense RD 30 abr 2024