Askey-Wilson polynomials as zonal spherical functions on the SU (2) quantum group

@article{Koornwinder1990AskeyWilsonPA,
  title={Askey-Wilson polynomials as zonal spherical functions on the SU (2) quantum group},
  author={T. Koornwinder},
  journal={Siam Journal on Mathematical Analysis},
  year={1990},
  volume={24},
  pages={795-813}
}
  • T. Koornwinder
  • Published 1990
  • Mathematics
  • Siam Journal on Mathematical Analysis
On the $SU(2)$ quantum group the notion of (zonal) spherical element is generalized by considering left and right invariance in the infinitesimal sense with respect to twisted primitive elements of the $sl(2)$ quantized universal enveloping algebra. The resulting spherical elements belonging to irreducible representations of quantum $SU(2)$ turn out to be expressible as a two-parameter family of Askey–Wilson polynomials. For a related basis change of the representation space a matrix of dual q… Expand

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