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The para-Racah polynomials
Jean-Michel Lemay, Luc Vinet, Alexei Zhedanov
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The…
An algebraic interpretation of the multivariate -Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet
The multivariate quantum -Krawtchouk polynomials are shown to arise as matrix elements of "-rotations" acting on the state vectors of many -oscillators. The focus is put o…
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke al…
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
The algebraic underpinning of the tridiagonalization procedure is investigated. The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadrat…