JORDAN ALGEBRAS AND ORTHOGONAL POLYNOMIALS

@article{Tsujimoto2011JORDANAA,
  title={JORDAN ALGEBRAS AND ORTHOGONAL POLYNOMIALS},
  author={Satoshi Tsujimoto and Luc Vinet and Alexei S. Zhedanov},
  journal={Journal of Mathematical Physics},
  year={2011},
  volume={52},
  pages={103512}
}
We illustrate how Jordan algebras can provide a framework for the interpretation of certain classes of orthogonal polynomials. The big −1 Jacobi polynomials are eigenfunctions of a first order operator of Dunkl type. We consider an algebra that has this operator (up to constants) as one of its three generators and whose defining relations are given in terms of anticommutators. It is a special case of the Askey-Wilson algebra AW(3). We show how the structure and recurrence relations of the big… Expand
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