Canonical realizations of Lie algebras associated with foliated coadjoint orbits
Dittmann, Jochen ; Rudolph, Gerd
Annales de l'I.H.P. Physique théorique, Tome 43 (1985), p. 251-267 / Harvested from Numdam
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Publié le : 1985-01-01
@article{AIHPA_1985__43_3_251_0,
     author = {Dittmann, Jochen and Rudolph, Gerd},
     title = {Canonical realizations of Lie algebras associated with foliated coadjoint orbits},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {43},
     year = {1985},
     pages = {251-267},
     mrnumber = {824841},
     zbl = {0605.58023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1985__43_3_251_0}
}

Dittmann, Jochen; Rudolph, Gerd. Canonical realizations of Lie algebras associated with foliated coadjoint orbits. Annales de l'I.H.P. Physique théorique, Tome 43 (1985) pp. 251-267. http://gdmltest.u-ga.fr/item/AIHPA_1985__43_3_251_0/

[1] P. Cordero, G.C. Ghirardi, Realizations of Lie algebras and algebraic treatment of quantum problems, Fortschr. Phys., t. 20, 1972, p. 105-133. | MR 449223

[2] L.M. Alonso, Group-theoretical foundations of classical and quantum mechanics. I. Observables associated with Lie algebras, J. Math. Phys., t. 18, 1977, p. 1577-1581. | MR 673018 | Zbl 0373.22012

[3] V. Guillemin, S. Sternberg, The moment map and collective motion, Ann. Phys., t. 127, 1, 1980, p. 220-257. | MR 576424 | Zbl 0453.58015

[4] A. Barut, R. Raczka, Theory of group representations and applications, Warszawa, PWN Polish Sci. Publ., 1977. | MR 495836

[5] P. Exner, M. Havlicek, W. Lassner, Canonical realizations of classical Lie algebras, Czech. J. Phys. B, t. 26, 1976, p. 1213-1228. | MR 430006 | Zbl 0381.17008

[6] I.M. Gelfand, A.A. Kirillov, Sur les corps lies aux algèbres enveloppantes des algèbres de Lie, Inst. Hautes Études Sci. Publ. Math., t. 31, 1966, p. 509-523. | Numdam | MR 207918 | Zbl 0144.02104

[7] A. Joseph, Minimal realizations and spectrum generating algebras, Comm. Math. Phys., t. 36, 36, 1974, p. 325-337. | MR 342049 | Zbl 0285.17007

[8] A.A., Kirillov, Эиеиенти теории представлений, изд. « Hayкa ». MOCКBa, 1972.

[9] B. Kostant, Quantization and unitary representations, in Lect. Notes Math., Vol. 170, Berlin-Heidelberg-New York, Springer-Verlag, 1972. | MR 294568 | Zbl 0223.53028

[10] D.J. Simms, N.M.J. Woodhouse, Lectures in geometric quantization, in Lect. Notes Phys., Vol. 53, Berlin-Heidelberg-New York, Springer-Verlag, 1976. | MR 672639 | Zbl 0343.53023

[11] A. Weinstein, Symplectic manifolds and their Lagrangean submanifolds, Advanc. Math., t. 6, 1971, p. 329-346. | MR 286137 | Zbl 0213.48203

[12] A. Weinstein, Lectures on symplectic manifolds, CBMS, no. 29, Rhode Island AMS, 1979. | MR 598470 | Zbl 0406.53031

[13] V. Guillemin, S. Sternberg, Geometric asymptotics, Math. surveys, no. 14, Rhode Island AMS, Providence, 1977. | MR 516965 | Zbl 0364.53011

[14] R. Bott, Lectures on characteristic classes and foliations, in Lect. Notes Math., t. 279, Berlin-Heidelberg-New York, Springer-Verlag, 1972. | MR 362335 | Zbl 0233.00013 | Zbl 0241.57010

[15] J. Kijowski, Geometrical structure of quantization, in Lect. Notes Math., t. 570, Berlin-Heidelberg-New York, Springer-Verlag, 1976. | MR 461571 | Zbl 0347.53017

[16] J. Dieudonné, Éléments d'Analyse, Tome 4, 2e édition, Gauthier-Villars Éditeur, Paris/Bruxelles/Montréal, 1974.

[17] M. Havliček, W. Lassner, Canonical realizations of the Lie algebras gl(n, R) and sl(n, R), Rep. Math. Phys., t. 8, no. 3, 1975. | MR 409575 | Zbl 0324.17002

[18] J. Dittmann, G. Rudolph, Canonical realizations of Lie algebras related to associated bundles, Proc. of the Conf. on Diff. Geom. and its Applic., Nové Mĕsto, 1983, p. 51-59. | MR 793199 | Zbl 0564.58017

[19] J. Dittmann, G. Rudolph, Konstruktion Kanonischer Realisierungen der Lie-Algebra sp(n, R) auf koadjungierten Orbits, Wiss. Z. KMU Leipzig, Math.- Naturwiss. R., t. 33, 1984, 1, p. 4-13. | MR 742612 | Zbl 0539.58010

[20] J. Dittmann, G. Rudolph, Canonical realizations of Lie algebras and coadjoint orbits. Part I. Lagrangean foliations of symplectic manifolds, prepr. KMU-OFT 06/82, Leipzig, 1982.

[21] J. Dittmann, G. Rudolph, Canonical realizations of Lie algebras and coadjoint orbits. Part II. Canonical realizations related to coadjoint orbits, prepr. KMU-QFT 03/83, Leipzig, 1983.

[22] P. Dazord, Sur la géométrie des sous-fibrés et des feuilletages lagrangiens, Ann. Scient. Ec. Norm. Sup. 4e série, t. 13, 1981, p. 465-480. | Numdam | MR 654208 | Zbl 0491.58015

[23] P. Dazord, Feuilletages en géométrie symplectique, C. R. Acad. Sci. Paris, t. 294, 1982, p. 489-491. | MR 679560 | Zbl 0509.58035

[24] P. Dazord, Feuilletages et mécanique hamiltonienne, Publ. Dép. Math. Univ. de Lyon, 1983, 3. B. | Numdam | MR 725514 | Zbl 0524.58016