Skip to main content
Log in

On the spherical and zonal spherical functions on a compact quantum group

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

Invariance properties of the functions satisfying an integral spherical equation on a compact quantum group are discussed. It is shown that spherical and zonal spherical functions are conncected with the spherical representation of a compact quantum group.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Koornwinder, T. H., Representations of the twisted SU(2) group and some q-hypergeometric orthogonal polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 92, 97–117 (1989).

    Google Scholar 

  2. Koornwinder, T. H., The addition formula for litte q-Legendre polynomials and the SU(2) quantum group, CWI Rep. AM-R8906, preprint, 1989.

  3. Koornwinder, T. H., Orthogonal polynomials in connection with quantum groups. CWI, preprint, 1989.

  4. Maurin, K., General Eigenfunction Expansions and Unitary Representations of Topological Groups, PWN, Warsaw, 1968.

    Google Scholar 

  5. Olshanecky, M. A. and Perelomov, A. M., Classical integrable finite dimensional systems related to Lie algebras, Phys. Rep. 5, 313–400 (1981).

    Google Scholar 

  6. Olshanecky, M. A. and Perelomov, A. M., Quantum integrable systems related to Lie algebras, Phys. Rep. 6, 314–404 (1983).

    Google Scholar 

  7. Podleś, P., Quantum spheres, Lett. Math. Phys. 14, 193–202 (1987).

    Google Scholar 

  8. Podleś, P., Quantum spaces and their symmetry groups, PhD thesis, Dept. Math. Meth. Phys. Warsaw University, 1990 (in Polish).

  9. Vilenkin, N. Ya., Special Functions and the Theory of Group Representations, Amer. Math. Soc. Transl. Math. Monographs, Vol. 22, 1968.

  10. Warner, G., Harmonic Analysis on Semi-simple Lie Groups I, II. Springer-Verlag, Berlin, 1972.

    Google Scholar 

  11. Wawrzyńczyk, A., Group Representations and Special Functions, PWN, Warsaw, 1984.

    Google Scholar 

  12. Woronowicz, S. L., Compact quantum groups, in preparation.

  13. Woronowicz, S. L., Compact matrix pseudogroups, Comm. Math. Phys. 111, 613–665 (1987).

    Google Scholar 

  14. Woronowicz, S. L., Twisted SU(2) group, an example of a non-commutative differential calculus. Publ. RIMS, Kyoto Univ. 23(1), 11 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by Polish Scientific Grant RPI10.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bragiel, K. On the spherical and zonal spherical functions on a compact quantum group. Lett Math Phys 22, 195–201 (1991). https://doi.org/10.1007/BF00403545

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00403545

AMS subject classifications (1991)

Navigation