Elements of the theory of induced representations 1 for quantum groups (original) (raw)

Abstract

We analyze the elements characterizing the theory of induced representations of Lie groups, in order to generalize it to quantum groups. We emphasize the geometric and algebraic aspects of the theory, because they are more suitable for generalization in the framework of Hopf algebras. As an example, we present the induced representations of a quantum deformation of the extended Galilei algebra in (1 + 1) dimensions.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (26)

  1. B. Parshall and J.P. Wang , Memoirs Amer.Math.Soc. 89, N.439 (1991).
  2. A. González-Ruiz and L.A. Ibort, Phys. Lett. B 296, 104 (1992).
  3. A.R. Gover and R.B. Zhang, Geometry of Quantum Homogeneous Vector Bundles and Representation Theory of Quantum Groups I, preprint q-alg 9705016.
  4. N. Ciccoli, Induction of quantum groups representations, preprint math/9804138.
  5. P. Maślanka, J. Math. Phys. 35, 5047 (1994).
  6. C. Gonera, P. Kosinski, P. Maślanka and M. Tarlini, J. Phys. A 31, 8473 (1998).
  7. F. Bonechi, R. Giachetti, E. Sorace and M. Tarlini, Lett. Math. Phys. 43, 309 (1998).
  8. L. Dabrowski and J. Sobczyk, Lett. Math. Phys. 32, 249 (1994).
  9. D. Ellinas and J. Sobczyk, J. Math. Phys. 36, 1404 (1995).
  10. O. Arratia and M.A. del Olmo, "Induced representations of quantum groups" in Geometry and Physics. Anales de Física. Monografías pp. 37-49. Ed. M. Asorey and J.F. Cariñena, CIEMAT/RSEF Madrid (1998).
  11. O. Arratia, Induced Representations of Quantum Algebras. Ph.D. Thesis, Universidad de Valladolid 1999 (in Spanish).
  12. O. Arratia and M.A. del Olmo, 41, 4817 (2000).
  13. A.A. Kirillov, Elements of the Theory of Representations, Springer, Berlin (1976).
  14. V. Chari and A. Pressley,A guide to quantum groups, Cambridge Univ. Press, Cam- bridge (1994).
  15. V.G. Drinfel'd, Quantum Groups. Proceedings of the Intern. Congress of Math., pp. 798, MRSI, Berkeley (1986).
  16. M. Jimbo, Lett. Math. Phys. 10, 63 (1985); 11, 247 (1986).
  17. N.Yu. Reshetikhin, L.A. Takhtadzhyan and L.D. Fadeev, Leningrad Math. J. 1, 193 (1990).
  18. S. L. Woronowicz, Comm. Math. Phys. 111, 613 (1987).
  19. S. Majid, Foundations of quantum group theory, Cambridge Univ. Press, Cambridge (1995).
  20. R. Molnar, J. Algebra, 47, 29 (1977).
  21. F. Bonechi, R. Giachetti, M. A. del Olmo, E. Sorace and M. Tarlini, J. Phys. A: Math. Gen. 29, 7973 (1996).
  22. P. Podles, Lett. Math. Phys. 14, 107 (1987).
  23. J. Dixmier, Algébres enveloppantes, Cahiers Scientifiques XXXVII, Gauthier-Villars, Paris (1974).
  24. D. G. Higman, Canad. J. Math. 7, 490 (1995).
  25. F. Bonechi, E. Celeghini, R. Giachetti, E. Sorace and M. Tarlini, Phys. Rev. B 46, 5727 (1992);
  26. J. Phys. A: Math. Gen. 25, L939 (1992).