Unitary representations of the quantum Lorentz group and quantum relativistic Toda chain

Theoretical and Mathematical Physics

Volumn 130, Issue 3, 2002, Pages 299-322

  Olshanetsky, M A ^a,b   Rogov, V B K ^c  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

^c RUSSIAN UNIVERSITY OF TRANSPORT   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036243609     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014713604396     Document Type: Article

References (36)

1. M. Olshanetsky and A. Perelomov, Phys. Rep., 94, 313 (1983).
2. N. Ya. Vilenkin, Special Functions and the Theory of Group Representations [in Russian], Nauka, Moscow (1991); English transl., Am. Math. Soc., Providence, R. I. (1968).
3. N. Ya. Vilenkin, Special Functions and the Theory of Group Representations [in Russian], Nauka, Moscow (1991); English transl., Am. Math. Soc., Providence, R. I. (1968).
4. B. Kostant, Invent. Math., 48, 101 (1978).
5. M. Semyonov-Tyan'-Shan'skii (Semenov-Tian-Shansky), "Quantization of open Toda chains [in Russian]," in: Contemporary Problems in Mathematics: Fundamental Directions (R. V. Gamkrelidze, ed.), Vol. 16, Dynamic Systems 7, VINITI, Moscow (1987), p. 194.
6. A. Gerasimov et al., Int. J. Mod. Phys. A, 12, 2523 (1997).
7. B. Feigin and E. Frenkel, Int. J. Mod. Phys. A, 7, Suppl. 1A, 197 (1992).
8. R. Goodman and N. Wallach, Trans. Am. Math. Soc., 315, 1 (1989).
9. T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, and K. Ueno, C. R. Acad. Sci., Paris, Ser. 1, Math., 307, 559 (1988).
10. L. Vaksman, Proc. Japan Acad. Ser. A. Math. Sci, 65, 169 (1989).
11. L. L. Vaksman and L. I. Korogodskii, Sov. Math. Dokl., 39, 173 (1989).
12. M. A. Olshanetsky and V.-B. K. Rogov, J. Phys. A, 27, 4669 (1994).
13. P. Podleś and S. L. Woronowicz, Commun. Math. Phys., 130, 381 (1990).
14. S. Ruijsenaars, Commun. Math. Phys., 133, 217 (1990).
15. M. A. Ol'shanetskii and V.-B. K. Rogov, Sb. Math., 187, 1525 (1996).
16. M. A. Ol'shanetskii and V.-B. K. Rogov, Sb. Math., 188, 1235 (1997).
17. V.-B. K. Rogov, "The integral representations of the q-Bessel Macdonald functions," math.QA/0101259 (2001); Preprint ITEP-TH-06/01, ITEP, Moscow (2001).
18. Pavel Etingof, "Whittaker functions on quantum groups and q-deformed Toda operators," math.QA/9901053 (1999).
19. A. Sevostyanov, "Quantum deformation of Whittaker modules and Toda lattice," math.QA/9905128 (1999).
20. q (sl(2, R)), the modular double, and the multiparticle q-deformed Toda chains," hep-th/0102180 (2001).
21. I. M. Gelfand, M. I. Graev, and N. Y. Vilenkin, Integral Geometry and Related Questions in Representation Theory [in Russian] (Vol. 5 of Generalized Functions and Operations on Them by I. M. Gelfand and G. E. Shilov.), Fizmatzig, Moscow (1962); English transl.: Integral Geometry and Representation Theory, (Vol. 5 of Generalized Functions by I. M. Gelfand and G. E. Shilov), Acad. Press, New York (1966).
22. I. M. Gelfand, M. I. Graev, and N. Y. Vilenkin, Integral Geometry and Related Questions in Representation Theory [in Russian] (Vol. 5 of Generalized Functions and Operations on Them by I. M. Gelfand and G. E. Shilov.), Fizmatzig, Moscow (1962); English transl.: Integral Geometry and Representation Theory, (Vol. 5 of Generalized Functions by I. M. Gelfand and G. E. Shilov), Acad. Press, New York (1966).
23. S. L. Woronowicz and S. Zakrzewski, Publ. RIMS, Kyoto Univ., 28, 809 (1992).
24. S. L. Woronowicz and S. Zakrzewski, Compos. Math., 90, 211 (1994).
25. N. Reshetikhin, L. Takhtadzhyan, and L. Faddeev, Leningrad Math. J., 1, 193 (1990); L. Faddeev, N. Reshetikhin, and L. Takhtajan, "Quantization of Lie groups and Lie algebras," in: Algebraic Analysis (M. Kashiwara and T. Kawai, eds.), Vol. 1, Acad. Press, Boston, Mass. (1988), p. 129.
26. N. Reshetikhin, L. Takhtadzhyan, and L. Faddeev, Leningrad Math. J., 1, 193 (1990); L. Faddeev, N. Reshetikhin, and L. Takhtajan, "Quantization of Lie groups and Lie algebras," in: Algebraic Analysis (M. Kashiwara and T. Kawai, eds.), Vol. 1, Acad. Press, Boston, Mass. (1988), p. 129.
27. V. Drinfeld, Leningrad Math. J., 1, 1419 (1990).
28. N. Reshetikhin, Lett. Math. Phys., 20, 331 (1990).
29. W. Pusz, Commun. Math. Phys., 152, 591 (1993).
30. L. Dabrovsky, V. Dobrev, and R. Floreanini, J. Math. Phys., 35, 971 (1994).
31. F. H. Jackson, Proc. London Math. Soc. (2), 2, 192 (1905).
32. H. T. Koelink, Duke Math. J., 76, 483 (1994).
33. A. Mironov, "Quantum deformations of τ-functions, bilinear identities, and representation theory," hep-th/9409190 (1994).
34. A. Morozov and L. Vinet, "Free field representation of group element for simple quantum groups," hep-th/9409093 (1994).
35. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge (1990).
36. V.-B. K. Rogov, "q-Bessel Macdonald functions," math.QA/ 0010170 (2000); Preprint ITEP-TH-56/00, Inst. Theor. Exp. Phys., Moscow (2000).