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arXiv · 2104.13960

Orthogonal polynomials and the deformed Jordan plane

André Beaudoin·Geoffroy Bergeron·Antoine Brillant·Julien Gaboriaud·Luc Vinet·Alexei Zhedanov
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Abstract

We consider the unital associative algebra $\mathcal{A}$ with two generators $\mathcal{X}$, $\mathcal{Z}$ obeying the defining relation $[\mathcal{Z},\mathcal{X}]=\mathcal{Z}^2+\Delta$. We construct irreducible tridiagonal representations of $\mathcal{A}$. Depending on the value of the parameter $\Delta$, these representations are associated to the Jacobi matrices of the para-Krawtchouk, continuous Hahn, Hahn or Jacobi polynomials.

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André Beaudoin, Geoffroy Bergeron, Antoine Brillant, Julien Gaboriaud, Luc Vinet, Alexei Zhedanov. 2021-04-28. Orthogonal polynomials and the deformed Jordan plane. https://doi.org/10.1016/j.jmaa.2021.125717

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