Advertisement

Askey-wilson polynomials as spherical functions on SUq(2)

  • Masatoshi Noumi
  • Katsuhisa Mimachi
I. Quantum Groups, Deformation Theory And Representation Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1510)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AW]
    Askey R. and Wilson J., Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Am. Math. Soc. 54 no. 319 (1985).Google Scholar
  2. [D]
    Drinfeld V.G., Quantum groups, Proc. IMC-86, 1 (1987), 798–820, Berkely.MathSciNetGoogle Scholar
  3. [J]
    Jimbo M., A q-difference analogue of U(G) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63–69.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [K1]
    Koornwinder T.H., Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials, Proc. K. Ned. Akad. Wet., Ser.A 92 (1989), 97–117.MathSciNetzbMATHGoogle Scholar
  5. [K2]
    Koornwinder T.H., Continuous q-Legendre polynomials as spherical matrix elements of irreducible representations of the quantum SU(2) group, CWI Quaterly 2 (1989), 171–173.zbMATHGoogle Scholar
  6. [K3]
    Koornwinder T.H., Orthogonal polynomials in connections with quantum groups, in Orthogonal Polynomials, Theory and Practice ed. P.Nevai, NATO ASI Series (1990), 257–292, Kluwer Academic Publishers.Google Scholar
  7. [K4]
    Koornwinder T.H., Askey-Wilson polynomials as zonal spherical functions on the quantum group SU q(2), Preprint (1990).Google Scholar
  8. [Ko]
    Korogodsky L.I., Quantum projective spaces, spheres and hyperboloids, Preprint (1990).Google Scholar
  9. [M]
    Masuda T.,Mimachi K., Nakagami Y., Noumi M. and Uneo K., Representations of the quantum group SU q (2) and the little q-Jacobi polynomials, J. Funct. Anal. (to appear).Google Scholar
  10. [NM1]
    Noumi M. and Mimachi K., Quantum 2-spheres and big q-Jacobi polynomials, Commun. Math. Phys. 128 (1990), 521–531.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [NM2]
    Noumi M. and Mimachi K., Big q-Jacobi polynomials, quantum 3-spheres, Lett. Math. Phys. 19 (1990), 299–305.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [NM3]
    Noumi M. and Mimachi K., Spherical functions on a family of quantum 3-spheres, Preprint (1990).Google Scholar
  13. [NM4]
    Noumi M. and Mimachi K., Rogers' q-ultraspherical polynomials on a quantum 2-sphere, Preprint (1990).Google Scholar
  14. [NM5]
    Noumi M. and Mimachi K., Askey-Wilson polynomials and the quantum group SU q(2), Proc. Japan Acad. Ser.A 66 (1990), 146–149.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [P]
    Podles P., Quantum spheres, Lett. Math. Phys. 14 (1987), 193–202.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [VS]
    Vaksman L.L. and Soibelman Ya.S., Algebra of functions on the quantum SU(2) group, Funkz. Anal. Pril. 22 (1988), 1036–1040. (in Russian)MathSciNetGoogle Scholar
  17. [W]
    Woronowicz S.L., Twisted SU(2) group. An example of non-commutative differential calculus, Publ. RIMS 23 (1987), 117–181, Kyoto Univ.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Masatoshi Noumi
    • 1
  • Katsuhisa Mimachi
    • 2
  1. 1.Department of MathematicsCollege of Arts and Sciences University of TokyoTokyoJapan
  2. 2.Department of MathematicsNagoya UniversityNagoyaJapan

Personalised recommendations