Spherical functions on a family of quantum 3-spheres
Noumi, Masatoshi ; Mimachi, Katsuhisa
Compositio Mathematica, Tome 84 (1992), p. 19-42 / Harvested from Numdam
@article{CM_1992__83_1_19_0,
     author = {Noumi, Masatoshi and Mimachi, Katsuhisa},
     title = {Spherical functions on a family of quantum 3-spheres},
     journal = {Compositio Mathematica},
     volume = {84},
     year = {1992},
     pages = {19-42},
     mrnumber = {1168121},
     zbl = {0760.33009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1992__83_1_19_0}
}
Noumi, Masatoshi; Mimachi, Katsuhisa. Spherical functions on a family of quantum 3-spheres. Compositio Mathematica, Tome 84 (1992) pp. 19-42. http://gdmltest.u-ga.fr/item/CM_1992__83_1_19_0/

[AA0] G.E. Andrews and R. Askey: Classical orthogonal polynomials, Lecture note in math. 1171, Springer, 1985, 36-62. | MR 838970 | Zbl 0596.33016

[AA1] G.E. Andrews and R. Askey: Another q-extension of the beta function, Proc. Amer. Math. Soc. 81, 1981, 97-100. | MR 589145 | Zbl 0471.33001

[AW] R. Askey and J. Wilson: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985). | MR 783216 | Zbl 0572.33012

[B] G.M. Bergman: The diamond lemma for ring theory, Adv. in Math. 29, 178-218 (1978). | MR 506890 | Zbl 0377.16013

[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). | MR 1026957 | Zbl 0742.17018

[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. Ser A 92, 443-456 (1989). | Zbl 0708.22007

[K] T.H. Koornwinder: Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 92, 97-117 (1989). | MR 993682 | Zbl 0681.22020

[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. | MR 967361 | Zbl 0658.22010

[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). | MR 1121618 | Zbl 0737.33012

[NM0] M. Noumi and K. Mimachi: Quantum 2-spheres and big q-Jacobi polynomials, Commun. Math. Phys. 128, 521-531 (1990). | MR 1045882 | Zbl 0699.33005

[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). | MR 1051812 | Zbl 0749.33010

[S] D. Stanton: Some q-Krawtchouk polynomials on Chevalley groups, Amer. J. Math., 102, 625-662 (1980). | MR 584464 | Zbl 0448.33019

[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). | MR 1008117 | Zbl 0693.33006

[VS] L.L. Vaksman And Ya. S. Soibelman: Algebra of functions on the quantum group SU(2), Functional Anal. Appl. 22, 170-181 (1988). | MR 961757 | Zbl 0679.43006