Orbit method for the algebras of functions on quantum groups and coherent states. i

International Mathematics Research Notices

Volumn 1993, Issue 6, 1993, Pages 151-163

  Soibelman, Yan ^a  

^a HARVARD UNIVERSITY   (United States)

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[No Author keywords available]

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EID: 84963044023     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/S1073792893000169     Document Type: Article

References (18)

1. F. BEREZIN, General concept of quantization, Comm. Math. Phys. 40 (1975), 253-274.
2. V. DRINFELD, Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations, Dokl. Akad. Nauk. SSSR 268 (1983), 285-287.
3. V. DRINFELD, "Quantum groups" in Proceedings of the International Contess of Mathematicians, Berkeley, Volume 2, American Mathematical Society, Providence, 1987, 789-820.
4. B. JURCO AND P. STOVITEK, Quantum dressing orbits on compact groups, preprint, 1992.
5. L. KOROGODSKY, Quantum group SU(1, 1) x 2and beyond, preprint, Massachusetts Institute of Technology, 1993.
6. A. KIRILLOV, Elements of the Theory of Representations, Grundlehren Math. Wiss. 220, Springer-Verlag, Berlin, Berlin, 1976.
7. B. KOSTANT, "Quantization and unitary representation" in Lectures in Modern Analysis and Applications III, Lecture Notes in Math. 170, Springer-Verlag, Berlin, 1970, 87-208.
8. L. KOROGODSKY AND L. VAKSMAN, Harmonic analysis on quantum hyperboloids, preprint, Institute Teor. Phys. 90-27P, Kiev, 1990.
9. S. LEVENDORSKII AND Y. SOIBELMAN, Algebras offunctions on compact quantum groups, Schubert cells and quantum tori, Comm. Math. Phys. 139 (1991), 141-170.
10. J. RAWNSLEY, Coherent states and Kihler manifolds, Quart. J. Math. Oxford Ser. (2) 25 (1977), 403-415.
11. Y. SOIBELMAN, Algebra offunctions on quantum group SU(n) and Schubert cells, Soviet Math. Dokl. 40 (1990), 34-38.
12. Y. SOIBELMAN, Algebra of functions on a compact quantum group and its representations, Algebra Analiz 2:1 (1990), 190-212. Translated in Leningrad Math. J. 2 (1991), 161-178.
13. Y. SOIBELMAN, "Selected topics in quantum groups, lectures for the European school of group theory" in Infinite Analysis, Volume 2, Adv. Ser. Math. Phys. 16, World Scientific, Singapore, 1992.
14. Y. SOIBELMAN, "Two problems in quantized algebras of functions" in Quantum Groups, Lecture Notes in Math. 1510, Springer-Verlag, Berlin, 1992, 393.
15. Y. SOIBELMAN AND L. VAKSMAN, Algebra offunctions on the quantum group SU(2), Functional Anal. Appl. 22 (1988), 170-181.
16. Y. SOIBELMAN AND L. VAKSMAN, Algebra offunctions on quantum group SU(n + 1) and odd-dimensional quantum spheres, Algebra Analiz. 2:5 (1990), 101-120, translated in Leningrad Math. J. 2 (1991), 1023-1042.
17. Y. SOIBELMAN AND L. VAKSMAN, "Some problems in quantum groups" in Representation Theory and Dynamical Systems, Adv. in Soviet Math. 9, American Mathematical Society, Providence, 1992, 3-55.
18. A. WEINSTEIN, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), 523-557.