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Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra


Authors: Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet and Alexei Zhedanov
Journal: Proc. Amer. Math. Soc. 144 (2016), 4441-4454
MSC (2010): Primary 33C45, 33C80, 42C05
DOI: https://doi.org/10.1090/proc/13082
Published electronically: April 27, 2016
MathSciNet review: 3531193
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Abstract: The algebraic underpinning of the tridiagonalization procedure is investigated. The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadratic Jacobi algebra. It is shown that under tridiagonalization, the quadratic Jacobi algebra becomes the quadratic Racah-Wilson algebra associated to the generic Racah-Wilson polynomials. A degenerate case leading to the Hahn algebra is also discussed.


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Additional Information

Vincent X. Genest
Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7 Canada
Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
Email: vxgenest@mit.edu

Mourad E. H. Ismail
Affiliation: Department of Mathematics, King Saud University, Riyadh, Saudi Arabia–and– Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: mourad.eh.ismail@gmail.com

Luc Vinet
Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7 Canada
Email: vinetl@crm.umontreal.ca

Alexei Zhedanov
Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7 Canada
Email: zhedanov@yahoo.com

DOI: https://doi.org/10.1090/proc/13082
Received by editor(s): June 25, 2015
Received by editor(s) in revised form: December 29, 2015
Published electronically: April 27, 2016
Communicated by: Walter Van Assche
Article copyright: © Copyright 2016 American Mathematical Society