Geodesic
Invariant operators for the classical groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 344-347 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Eigenvalues of the invariant operators of arbitrary order are calculated for all classical groups. The eigenvalues are represented in the form of the polynomials over power sums $S_k$ (cf. the formulas (2.10)–(2.12)). 
@article{TMF_1977_32_3_a3,
     author = {V. S. Popov},
     title = {Invariant operators for the classical groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {344--347},
     year = {1977},
     volume = {32},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a3/}
}
TY  - JOUR
AU  - V. S. Popov
TI  - Invariant operators for the classical groups
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1977
SP  - 344
EP  - 347
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a3/
LA  - ru
ID  - TMF_1977_32_3_a3
ER  - 
%0 Journal Article
%A V. S. Popov
%T Invariant operators for the classical groups
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1977
%P 344-347
%V 32
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a3/
%G ru
%F TMF_1977_32_3_a3
V. S. Popov. Invariant operators for the classical groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 344-347. http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a3/

[1] E. P. Wigner, Ann. Math., 40 (1939), 149 | DOI | MR | Zbl

[2] G. Racah, Group Theory and Spectroscopy. Lecture notes, Princeton, 1951 | Zbl

[3] R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications, Wiley-Interscience, N. Y., 1974 | MR | Zbl

[4] B. G. Wybourne, Classical Groups for Physicists, Wiley, N. Y., 1974 | Zbl

[5] A. N. Leznov, M. V. Savelev, EChAYa, 7:1 (1976), 55 | MR

[6] V. S. Popov, TMF, 29 (1976), 137 | MR

[7] G. Veil, Klassicheskie gruppy, ikh invarianty i predstavleniya, IL, 1947

[8] D. P. Zhelobenko, UMN, 17 (1962), 27

[9] D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, «Nauka», 1970 | MR | Zbl

[10] J. D. Louck, H. W. Galbraith, Rev. Mod. Phys., 44 (1972), 540 | DOI | MR

[11] A. M. Perelomov, V. S. Popov, Pisma v ZhETF, 2 (1965), 34 ; ЯФ, 3 (1966), 1127 | MR | Zbl | MR

[12] V. S. Popov, A. M. Perelomov, YaF, 7 (1968), 460