Geodesic
On a complete set of commuting operators for ladder representations of the Lie algebra of
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 365-379 
A. B. Nikolov. On a complete set of commuting operators for ladder representations of the Lie algebra of. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 365-379. http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a6/
@article{TMF_1971_9_3_a6,
     author = {A. B. Nikolov},
     title = {On a~complete set of commuting operators for ladder representations of the {Lie} algebra of},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {365--379},
     year = {1971},
     volume = {9},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a6/}
}
TY  - JOUR
AU  - A. B. Nikolov
TI  - On a complete set of commuting operators for ladder representations of the Lie algebra of
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 365
EP  - 379
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a6/
LA  - ru
ID  - TMF_1971_9_3_a6
ER  - 
%0 Journal Article
%A A. B. Nikolov
%T On a complete set of commuting operators for ladder representations of the Lie algebra of
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 365-379
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a6/
%G ru
%F TMF_1971_9_3_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

In connection with applications of tlie ladder representations the question about the completeness of a set of commuting operators with a definite physical interpretation is investigated. A suitable transformation of these operators is introduced, by means of which the problem under consideration is reduced to investigation of a system of functional equations. A number of theorems about this system are proved, from which the completeness of the mentioned set follows. As a result, we have established that the ladder representations of the Lie algebra of $U(6,6)$ can be given in terms of a physical complete set of commuting operators.

[1] I. M. Gelfand, M. I. Graev, Izv. AN SSSR, seriya matem., 29 (1965), 1329 | MR | Zbl

[2] A. V. Nikolov, K. V. Rerikh, Preprint 5-2962, OIYaI, 1966

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

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

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

[6] Y. Dothan, M. Gell-Mann, Y. Ne'eman, Phys. Lett., 17 (1965), 148 | DOI | MR