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The non-symmetric Wilson polynomials are the Bannai-Ito polynomials

Authors: Vincent X. Genest, Luc Vinet and Alexei Zhedanov
Journal: Proc. Amer. Math. Soc. 144 (2016), 5217-5226
MSC (2010): Primary 33C80, 20C08
Published electronically: May 24, 2016
MathSciNet review: 3556266
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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 $ (C_1^{\vee }, C_1)$ 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.

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Additional Information

Vincent X. Genest
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Luc Vinet
Affiliation: Centre de recherches mathématiques, Université de Montréal, Montréal, QC, Canada H3C 3J7

Alexei Zhedanov
Affiliation: Donetsk Institute for Physics and Technology, Donetsk 83114, Ukraine

Received by editor(s): July 10, 2015
Received by editor(s) in revised form: February 8, 2016
Published electronically: May 24, 2016
Additional Notes: This work was presented on January 9, 2016 by the first author at the Joint Mathematics Meetings in the AMS Special Session on Special Functions and $q$-Series
Communicated by: Mourad Ismail
Article copyright: © Copyright 2016 American Mathematical Society

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