On q-analogues of bounded symmetric domains and dolbeault complexes

Mathematical Physics, Analysis and Geometry

Volumn 1, Issue 1, 1998, Pages 75-100

  Sinel'Shchikov, S ^a   Vaksman, L ^a  

^a B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

Author keywords

Quantum differential calculi; Quantum homogeneous spaces

Indexed keywords

EID: 0040912942     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009704002239     Document Type: Article

References (25)

1. Abe, E.: Hopf Algebras, Cambridge Univ. Press, Cambridge, 1980.
2. Bopp, P. N. and Rubenthaler, H.: Fonction zêta associée àla série principale sphérique de certain espaces symmétriques, Ann. Sci. École Nonn. Sup. (4) 26 (1993), 701-745.
3. Chari, V. and Pressley, A.: A Guide to Quantum Croups, Cambridge Univ. Press, Cambridge, 1995.
4. de Concini, C. and Kac, V.: Representations of quantum groups at roots of 1, in: A. Connes, M. Duflo, A. Joseph and R. Rentschier (eds), Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory, 1990, Birkhauser, Boston, pp. 471-506.
5. Dixmier, J.: Les C-algèbres et leur représentations, Gauthier-Villars, Paris, 1964.
6. Drinfeld, V. G.: Quantum groups, in: A. M. Gleason (ed), Proceedings of the International Congress of Mathematicians, Berkeley, 1986, American Mathematical Society, Providence, R.I., 1989, pp. 798-820.
7. Drinfeld, V. G.: On almost commutative Hopf algebras, Leningrad Math. J. 1 (1990), 321-432.
8. Helgason, S.: Differential Geometry and Symmetric Spaces, Acad. Press, NY, London, 1962.
9. Humphreys, J. E.: Reflection Groups and Coxeter Groups, Cambridge Univ. Press, 1990.
10. Joyal, A. and Street, R.: Braided tensor categories, Adv. in Math. 102 (1993), 20-78.
11. Kassel, C.: Quantum Groups, Springer-Verlag, NY, Berlin, Heidelberg, 1995.
12. Klimek, S. and Lesniewski, A.: A two-parameter quantum deformation of the unit disc, J. Funct. Anal. 115 (1993), 1-23.
13. Kelley, J. L. and Namioka, I.: Linear Typological Spaces, Van Nostrand Inc., Princeton, NY, London, 1963.
14. Khoroshkin, S., Radul, A. and Rubtsov, V.: A family of Poisson structures on compact Hermitian symmetric spaces, Comm. Math. Pliys. 152 (1993), 299-316.
15. Lustig, G.: Quantum groups at roots of 1, Geom. Dedicata 35 (1990), 89-114.
16. Levendorskii, S. Z. and Soibelman, Ya. S.: Some applications of the quantum Weil group, J. Geom. Pliys. 7 (1990), 241-254.
17. Maltsiniotis, G.: Le langage des espaces et des groupes quantiques, Comm. Math. Phys. 151 (1993), 275-302.
18. Nagy, G. and Nica, A.: On the 'quantum disc' and a 'non-commutative circle', in: R. E. Curto, P. E. T. Jorgensen (eds), Algebraic Methods on Operator Theory, Birkhauser, Boston, 1994, pp. 276-290.
19. Rubenthaler, H.: Les paires duales dans les algèbres de Lie réductives, Astérisque 219 (1994).
20. Serre, J. P.: Complex Semisimple Algebras, Springer, Berlin, Heidelberg, New York, 1987.
21. Sinel'shchikov, S. and Vaksman, L.: Hidden symmetry of the differential calculus on the quantum matrix space, to appear in J. Pliys. A.
22. Soibelman, Ya. S. and Vaksman, L. L.: On some problems in the theory of quantum groups, in: A. M. Vershik (ed), Representation Theory and Dynamical Systems, Advances in Soviet Mathematics 9, American Mathematical Society, Providence, RI (1990), pp. 3-55.
23. Sinel'shchikov, S., Shklyarov, D. and Vaksman, L.: On function theory in the quantum disc: Integral representations. Preprint, 1997, q-alg.
24. Vaksman, L. L. and Soibelman, Ya. S.: Algebra of functions on the quantum group SU(2), Funct. Anal. Appl. 22 (1988), 170-181.
25. Woronowicz, S. L.: Compact matrix pseudogroups, Comm. Math. Phys. Ill (1987), 613-665.