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Bannai-Ito polynomials and dressing chains


Authors: Maxim Derevyagin, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov
Journal: Proc. Amer. Math. Soc. 142 (2014), 4191-4206
MSC (2010): Primary 42C05; Secondary 17B80, 33C45, 47B36
Published electronically: August 1, 2014
MathSciNet review: 3266989
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Abstract: Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by quadratic algebras. The Bannai-Ito polynomials and their kernel polynomials - the complementary Bannai-Ito polynomials - are shown to arise in the framework of the SDG maps.


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Additional Information

Maxim Derevyagin
Affiliation: Department of Mathematics MA 4-2, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany
Address at time of publication: Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Box 2400, BE-3001 Leuven, Belgium

Satoshi Tsujimoto
Affiliation: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

Luc Vinet
Affiliation: Centre de recherches mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec, H3C 3J7, Canada

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

DOI: https://doi.org/10.1090/S0002-9939-2014-12165-4
Keywords: Darboux transformations, dressing chains, orthogonal polynomials, Schur-Delsarte-Genin map, Bannai-Ito polynomials, quadratic algebras
Received by editor(s): January 8, 2013
Published electronically: August 1, 2014
Additional Notes: The first author acknowledges the support of the European Research Council under the European Union Seventh Programme (FP/2007-2013)/ERC grant agreement No. 259173. The first and fourth authors thank the University of Montreal for its hospitality in the course of this study
The research of the third author was supported in part by a research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2014 American Mathematical Society