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References
Askey R. and Wilson J., Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Am. Math. Soc. 54 no. 319 (1985).
Drinfeld V.G., Quantum groups, Proc. IMC-86, 1 (1987), 798–820, Berkely.
Jimbo M., A q-difference analogue of U(G) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63–69.
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.
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.
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.
Koornwinder T.H., Askey-Wilson polynomials as zonal spherical functions on the quantum group SU q(2), Preprint (1990).
Korogodsky L.I., Quantum projective spaces, spheres and hyperboloids, Preprint (1990).
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).
Noumi M. and Mimachi K., Quantum 2-spheres and big q-Jacobi polynomials, Commun. Math. Phys. 128 (1990), 521–531.
Noumi M. and Mimachi K., Big q-Jacobi polynomials, quantum 3-spheres, Lett. Math. Phys. 19 (1990), 299–305.
Noumi M. and Mimachi K., Spherical functions on a family of quantum 3-spheres, Preprint (1990).
Noumi M. and Mimachi K., Rogers' q-ultraspherical polynomials on a quantum 2-sphere, Preprint (1990).
Noumi M. and Mimachi K., Askey-Wilson polynomials and the quantum group SU q(2), Proc. Japan Acad. Ser.A 66 (1990), 146–149.
Podles P., Quantum spheres, Lett. Math. Phys. 14 (1987), 193–202.
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)
Woronowicz S.L., Twisted SU(2) group. An example of non-commutative differential calculus, Publ. RIMS 23 (1987), 117–181, Kyoto Univ.
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© 1992 Springer-Verlag
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Noumi, M., Mimachi, K. (1992). Askey-wilson polynomials as spherical functions on SU q(2). In: Kulish, P.P. (eds) Quantum Groups. Lecture Notes in Mathematics, vol 1510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101182
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DOI: https://doi.org/10.1007/BFb0101182
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