Proceedings of the Japan Academy, Series A, Mathematical Sciences

Askey-Wilson polynomials and the quantum group ${SU}_q \left( 2 \right)$

Masatoshi Noumi and Katsuhisa Mimachi

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Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 66, Number 6 (1990), 146-149.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195512453

Digital Object Identifier
doi:10.3792/pjaa.66.146

Mathematical Reviews number (MathSciNet)
MR1065793

Zentralblatt MATH identifier
0707.33010

Subjects
Primary: 33D80: Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

Citation

Noumi, Masatoshi; Mimachi, Katsuhisa. Askey-Wilson polynomials and the quantum group ${SU}_q \left( 2 \right)$. Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 6, 146--149. doi:10.3792/pjaa.66.146. https://projecteuclid.org/euclid.pja/1195512453


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References

  • [1] R. Askey and J. Wilson: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc, 54, no. 319 (1985).
  • [2] T. H. Koornwinder: Orthogonal polynomials in connections with quantum groups. Orthogonal Polynomials, Theory and Practice (ed. P. Nevai). NATO ASI Series, Kluwer Academic Publishers, pp. 257-292 (1990).
  • [3] M. Noumi and K. Mimachi: Quantum 2-spheres and big g-Jacobi polynomials. Commun. Math. Phys, 128, 521-531 (1990).
  • [4] M. Rahman and A. Verma: Product and addition formulas for the continuous g-ultraspherical polynomials. SIAM J. Math. Anal., 17, 1461-1474 (1986).