Geodesic
Complete ladder sets for $U(6, 6)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 3, pp. 315-324 
I. S. Vaklev; S. B. Drenska; S. I. Zlatev; M. I. Ivanov; A. B. Nikolov. Complete ladder sets for $U(6, 6)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 3, pp. 315-324. http://geodesic.mathdoc.fr/item/TMF_1975_24_3_a2/
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     title = {Complete ladder sets for $U(6, 6)$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Complete sets of commuting (symmetric) operators which, belong to the enveloping algebra of an arbitrary ladder representation of the group $U(6, 6)$ are considered. These sets are independent and each of them includes the operators $B, n, Y, Z, I^2, I_3, J^2, J_3$ which possess a definite physical interpretation [3]. The proof of the completeness of the considered sets is the main result of the work. Besides this, a method is given for the construction of all common eigenvectors of each complete set.

[1] A. V. Nikolov, TMF, 9 (1971), 365 | MR | Zbl

[2] I. S. Vaklev, S. B. Drenska, M. I. Ivanov, A. V. Nikolov. TMF, TMF, 14 (1973), 56

[3] I. S. Vaklev, S. B. Drenska, M. I. Ivanov, A. V. Nikolov. TMF, TMF, 20 (1974), 78 | MR

[4] I. M. Gelfand, M. I. Graev, Izv. AN SSSR, seriya matem., 29 (1965), 1329 ; А. В. Николов, К. В. Рерих, Препринт ОИЯИ 5-2962, Дубна, 1966 | MR | Zbl

[5] I. T. Todorov, Preprint IC/66/71, ICTP, 1966

[6] A. M. Perelomov, V. S. Popov, YaF, 3 (1966), 924 | MR

[7] P. A. M. Dirak, Printsipy kvantovoi mekhaniki, Fizmatgiz, 1960 | MR