Quantum systems related to root systems, and radial parts of Laplace operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 12 (1978) no. 2, pp. 57-65.

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

@article{FAA_1978_12_2_a6,
     author = {M. A. Olshanetsky and A. M. Perelomov},
     title = {Quantum systems related to root systems, and radial parts of {Laplace} operators},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {57--65},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1978_12_2_a6/}
}
TY  - JOUR
AU  - M. A. Olshanetsky
AU  - A. M. Perelomov
TI  - Quantum systems related to root systems, and radial parts of Laplace operators
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1978
SP  - 57
EP  - 65
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1978_12_2_a6/
LA  - ru
ID  - FAA_1978_12_2_a6
ER  - 
%0 Journal Article
%A M. A. Olshanetsky
%A A. M. Perelomov
%T Quantum systems related to root systems, and radial parts of Laplace operators
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1978
%P 57-65
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1978_12_2_a6/
%G ru
%F FAA_1978_12_2_a6
M. A. Olshanetsky; A. M. Perelomov. Quantum systems related to root systems, and radial parts of Laplace operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 12 (1978) no. 2, pp. 57-65. http://geodesic.mathdoc.fr/item/FAA_1978_12_2_a6/

[1] Gelfand I.M., “Tsentr infinitezimalnogo gruppovogo koltsa”, Matem. sb., 26 (1950), 103–112 | MR

[2] Gelfand I.M., “Sfericheskie funktsii na simmetricheskikh rimanovykh prostranstvakh”, DAN SSSR, 70:1 (1950), 5–8

[3] Berezin F.A., “Operatory Laplasa na poluprostykh gruppakh Li”, Trudy Mosk. matem. ob-va, VI, 1957, 371–463 | MR

[4] Berezin F.A., Karpelevich F.I., “Zonalnye sfericheskie funktsii i operatory Laplasa na nekotorykh simmetricheskikh prostranstvakh”, DAN SSSR, 118:1 (1958), 9–12 | MR | Zbl

[5] Olshanetsky M.A., Perelomov A.M., “Completely integrable Hamiltonian systems connected with semisimple Lie algebras”, Invent. Math., 37 (1976), 93–108 | DOI | MR | Zbl

[6] Burbaki N., Gruppy i algebry Li, Mir, M., 1972 | MR | Zbl

[7] Calogero F., “Solution of a three-body problem in one dimension”, J. Math. Phys., 10 (1969), 2191–2196 | DOI | MR

[8] Calogero F., “Solution of the one-dimensional iV-body problem”, J. Math. Phys., 12 (1971), 419–436 | DOI | MR

[9] Perelomov A.M., “Algebraicheskii podkhod k resheniyu odnomernoi modeli $N$ vzaimodeistvuyuschikh chastits”, TMF, 6 (1971), 364–391 | MR

[10] Sutherland B. Exact, “results for a quantum manv-body problem in one dimension”, Phys. Rev., A5 (1972), 1372–1376 | DOI

[11] Gambardella P.J., “Exact results in quantum many-body systems of interacting particles”, J. Math. Phys., 16 (1975), 1172–1187 | DOI | MR

[12] Moshinsky M., Patera J., “Canonical transformations and accidental degeneracy. IV”, J. Math. Phys., 16 (1975), 1866–1875 | DOI | MR

[13] Galogero F., Marchioro C., Ragnisco O., “Exact solution of the classical and quantal one-dimensional many-body problem”, Lett. N.C., 13 (1975), 383–388 | DOI | MR

[14] Wolfes J., “On the three-body linear problem with three-body interaction”, J. Math. Phys., 15 (1974), 1420–1424 | DOI | MR

[15] Calogero F., Marchioro C., “Exact solution of three-body scattering problem”, J. Math. Phys., 15 (1974), 1425–1430 | DOI | MR

[16] Khelgason S., Differentsialnaya geometriya i simmetricheskie prostranstva, Mir, M., 1964

[17] Berezin F.A., Pokhil G.P., Finkelberg V.M., “Uravnenie Shredingera dlya sistemy odnomernykh chastits s tochechnym vzaimodeistviem”, Vestnik MGU, 1964, no. 1, 21–28 | MR

[18] Araki Sh., “Kornevye sistemy i lokalnaya klassifikatsiya neprivodimykh simmetricheskikh prostranstv”, Matematika, 10:1 (1966), 90–126 | MR

[19] Olshanetsky M.A., Perelomov A.M., “Quantum completely integrable systems connected with semisimple Lie algebras”, Lett. Math. Phys., 2 (1977), 7–13 | DOI | MR | Zbl