The non-symmetric Wilson polynomials are the Bannai-Ito polynomials
Classical Analysis and ODEs
2017-02-15 v1 Mathematical Physics
math.MP
Abstract
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 algebra of type and the Bannai-Ito algebra is established. The Bannai-Ito polynomials are seen to satisfy an orthogonality relation with respect to a positive-definite and continuous measure on the real line. A non-compact form of the Bannai-Ito algebra is introduced and a four-parameter family of its infinite-dimensional and self-adjoint representations is exhibited.
Keywords
Cite
@article{arxiv.1507.02995,
title = {The non-symmetric Wilson polynomials are the Bannai-Ito polynomials},
author = {Vincent X. Genest and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:1507.02995},
year = {2017}
}