Spherical functions on a family of quantum 3-spheres

Masatoshi Noumi; Katsuhisa Mimachi

Compositio Mathematica (1992)

  • Volume: 83, Issue: 1, page 19-42
  • ISSN: 0010-437X

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Noumi, Masatoshi, and Mimachi, Katsuhisa. "Spherical functions on a family of quantum 3-spheres." Compositio Mathematica 83.1 (1992): 19-42. <http://eudml.org/doc/90158>.

@article{Noumi1992,
author = {Noumi, Masatoshi, Mimachi, Katsuhisa},
journal = {Compositio Mathematica},
keywords = {quantum 3-spheres; quantum group; irreducible representations; spherical functions; big -Jacobi polynomials; -Hahn polynomials},
language = {eng},
number = {1},
pages = {19-42},
publisher = {Kluwer Academic Publishers},
title = {Spherical functions on a family of quantum 3-spheres},
url = {http://eudml.org/doc/90158},
volume = {83},
year = {1992},
}

TY - JOUR
AU - Noumi, Masatoshi
AU - Mimachi, Katsuhisa
TI - Spherical functions on a family of quantum 3-spheres
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 83
IS - 1
SP - 19
EP - 42
LA - eng
KW - quantum 3-spheres; quantum group; irreducible representations; spherical functions; big -Jacobi polynomials; -Hahn polynomials
UR - http://eudml.org/doc/90158
ER -

References

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  5. [KR] A.N. Kirillov and N. Yu. Reshetikhin: Representations of the algebra U q(sl(2)), q-orthogonal polynomials and invariants of links, in Infinite dimensional Lie algebras and groups, edited by V.G. Kac, World Scientific, 285-339 (1989). Zbl0742.17018MR1026957
  6. [KK] H.T. Koelink and T.H. Koornwinder: The Clebsch-Gordan coefficients for the quantum group Sμ U(2) and q-Hahn polynomials, Nederl. Akad. Wetensch. Proc. SerA92, 443-456 (1989). Zbl0708.22007
  7. [K] T.H. Koornwinder: Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials, Nederl. Akad. Wetensch. Proc. Ser.A92, 97-117 (1989). Zbl0681.22020MR993682
  8. [M0] T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi and K. Ueno: Representations of quantum groups and a q-analogue of orthogonal polynomials, C.R. Acad. Sci. Paris, 307, 1988, Série I, 559-564. Zbl0658.22010MR967361
  9. [M1] T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi and K. Ueno: Representations of the quantum group SU q(2) and the little q-Jacobi polynomials, J. Funct. Anal.99, 357-386 (1991). Zbl0737.33012MR1121618
  10. [NM0] M. Noumi and K. Mimachi: Quantum 2-spheres and big q-Jacobi polynomials, Commun. Math. Phys.128, 521-531 (1990). Zbl0699.33005MR1045882
  11. [NM1] M. Noumi and K. Mimachi: Big q-Jacobi polynomials, q-Hahn polynomials and a family of quantum 3-spheres, Lett. Math. Phys.19, 299-305 (1990). Zbl0749.33010MR1051812
  12. [S] D. Stanton: Some q-Krawtchouk polynomials on Chevalley groups, Amer. J. Math., 102, 625-662 (1980). Zbl0448.33019MR584464
  13. [V] L.L. Vaksman: q-Analogues of Clebsch-Gordan coefficients, and the algebra of functions on the quantum group SU(2), Soviet Math. Dokl., 39, 467-470 (1989). Zbl0693.33006MR1008117
  14. [VS] L.L. Vaksman and Ya. S. Soibelman: Algebra of functions on the quantum group SU(2), Functional Anal. Appl.22, 170-181 (1988). Zbl0679.43006MR961757

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