Geodesic
Identities and Invariant Operators on Homogeneous Spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 3, pp. 393-408 
I. V. Shirokov. Identities and Invariant Operators on Homogeneous Spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 3, pp. 393-408. http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a2/
@article{TMF_2001_126_3_a2,
     author = {I. V. Shirokov},
     title = {Identities and {Invariant} {Operators} on {Homogeneous} {Spaces}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {393--408},
     year = {2001},
     volume = {126},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a2/}
}
TY  - JOUR
AU  - I. V. Shirokov
TI  - Identities and Invariant Operators on Homogeneous Spaces
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 393
EP  - 408
VL  - 126
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a2/
LA  - ru
ID  - TMF_2001_126_3_a2
ER  - 
%0 Journal Article
%A I. V. Shirokov
%T Identities and Invariant Operators on Homogeneous Spaces
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 393-408
%V 126
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a2/
%G ru
%F TMF_2001_126_3_a2

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

We study identities (functional relations between the generators of the transformation group) and also algebras of invariant operators on homogeneous spaces using the method of orbits of the coadjoint representation (coadjoint orbits). This method permits establishing the relation between these two objects and elaborating an algorithm for their construction. A classification of homogeneous spaces is introduced based on the coadjoint orbit method.

[1] U. Miller, Simmetriya i razdelenie peremennykh, Mir, M., 1981 | MR

[2] V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, TMF, 83:1 (1990), 14–22 | MR | Zbl

[3] A. A. Kirillov, UMN, 17:4 (1962), 57–110 | MR | Zbl

[4] A. A. Kirillov, Elementy teorii predstavlenii, Nauka, M., 1978 | MR | Zbl

[5] A. A. Kirillov, “Vvedenie v teoriyu predstavlenii i nekommutativnyi garmonicheskii analiz”, Teoriya predstavlenii i nekommutativnyi garmonicheskii analiz, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 22, ed. R. V. Gamkrelidze, VINITI, M., 1988, 5–162 | MR

[6] I. V. Shirokov, TMF, 123:3 (2000), 407–423 | DOI | MR | Zbl

[7] A. V. Shapovalov, I. V. Shirokov, TMF, 104:2 (1995), 195–213 | MR | Zbl

[8] S. P. Baranovskii, V. V. Mikheev, I. V. Shirokov, Izv. vuzov. Fizika, 43:11 (2000), 72–78 | MR | Zbl

[9] I. V. Shirokov, $K$-orbity, garmonicheskii analiz na odnorodnykh prostranstvakh i integrirovanie differentsialnykh uravnenii, Preprint, OmGU, Omsk, 1998

[10] D. N. Akhiezer, E. B. Vinberg, Transformation Groups, 4:1 (1999), 3–24 | DOI | MR | Zbl