RT Journal Article T1 Commutativity of missing label operators in terms of Berezin brackets A1 Boya, Luis J. A1 Campoamor-Stursberg, Rutwig AB We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement of missing label operators for reduction chains in the missing label problem can be solved analytically PB IOP Publishing Ltd SN 1751-8113 YR 2009 FD 2009 LK https://hdl.handle.net/20.500.14352/43780 UL https://hdl.handle.net/20.500.14352/43780 LA eng NO Iachello F and Arima A 1987 The interacting boson model, (Cambridge Univ. Press, Cambridge).Elliott J P 1958 Proc. Roy. Soc. Lond. A 245 128, 562Helmers K 1961 Nuclear Phys. 23 594Moshinsky M and Nagel J G 1963 Phys. Letters 5 173Hecht K T 1994 J. Phys. A: Math. Gen. 27 3445Jarvis P D 1974 J. Phys. A: Math. Gen. 7 1807Sharp R T and Pieper S C 1968 J. Math. Phys. 9 663Sharp R T 1975 J. Math. Phys. 16, 2050Judd B R, Miller W, Patera J and Winternitz P 1974 J. Math. Phys. 15 1787Louck J D 1976 Proceedings of the International Symposium on Mathematical Physics, Mexico City,Mexico Jarvis P D and Zhang R B 2005 J. Phys. A: Math. Gen. 38 L219Quesne Ch 1976 J. Math. Phys. 17, 1452; 18, 1210 (1977)Partensky A and Maguin C 1978 J. Math. Phys. 19 511Bincer A M 1983 J. Math. Phys. 24 1695Van der Jeugt 1984 J. Math. Phys. 25 1221Hughes J W B and Van der Jeugt J 1985 J. Math. Phys. 26 894De Meyer H, Vanden Berghe G and De Wilde P 1987 Comput. Phys. Comm. 44 197von Isacker P and Juillet O 1999 Nuclear Phys. A564 739Valencia J P and Wu H C 2004 Braz. J. Phys. 34 837Wybourne B G 1992 J. Phys. B: At. Mol. Opt. 25 1683Peccia A and Sharp R T 1976 J. Math. Phys. 17 1313Vitiello G and de Concini C 1976 Nuclear Phys. B116 141Campoamor-Stursberg 2007 J. Phys. A: Math. Theor. 40 14773 (hep-th/arXiv:0706.2581)Campoamor-Stursberg R 2008 J. Phys. Conf. Ser. 128 012052Ol’shanskii’ G 1997 Transf. Groups 2 197Gaskell R, Rosensteel G and Sharp R T 1981 J. Math. Phys. 22 2732Racah G 1949 Phys. Rev. 76 1352 ——1951 Group Theory and Spectroscopy, (Princeton Univ. Press, New Jersey)Campoamor-Stursberg R 2007 J. Phys. A: Math. Theor. 40 5355Beltrametti E G and Blasi A 1966 Physics Letters 20 62Abellanas L and Martínez Alonso L 1975 J. Math. Phys. 16 1580Dixmier J 1974 Algebres enveloppantes (Gauthier-Villars, Paris)Berezin F A 1965 Metod vtorichnogo kvantovaniya (Nauka, Moscow)——1967 Funkt. Anal. Prolozh. 1 1Perelomov A M 1990 Integriruemye sistemy klassicheskoi’ mekhaniki i algebry Li (Glav. red. fiziko-matematicheskoi’ Lit-ry, Moscow)Graber J L and Rosensteel G 2003 Phys. Rev. C 68 014301Campoamor-Stursberg R 2005 J. Phys. A: Math. Gen. 38 4187Wybourne B G 1995 Lithuanian J. Phys. 35 123 NO CICYT (LJB) NO M.E.C. NO U.C.M.-C.A.M (RCS) DS Docta Complutense RD 27 abr 2024