Bispectrality of the Complementary Bannai-Ito Polynomials

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9, випуск за цей рік
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dc.contributor.author	Genest, V.X.
dc.contributor.author	Vinet, L.
dc.contributor.author	Zhedanov, A.
dc.date.accessioned	2019-02-19T19:01:13Z
dc.date.available	2019-02-19T19:01:13Z
dc.date.issued	2013
dc.identifier.citation	Bispectrality of the Complementary Bannai-Ito Polynomials / V.X. Genest, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 31 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 33C02; 16G02
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2013.018
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149225
dc.description.abstract	A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→−1 limit of the Askey-Wilson polynomials. The eigenvalue equations for the CBI polynomials are found to involve second order Dunkl shift operators with reflections and exhibit quadratic spectra. The algebra associated to the CBI polynomials is given and seen to be a deformation of the Askey-Wilson algebra with an involution. The relation between the CBI polynomials and the recently discovered dual −1 Hahn and para-Krawtchouk polynomials, as well as their relation with the symmetric Hahn polynomials, is also discussed.	uk_UA
dc.description.sponsorship	V.X.G. holds a scholarship from Fonds de recherche qu´eb´ecois – nature et technologies (FRQNT). The research of L.V. is supported in part by the Natural Science and Engineering Council of Canada (NSERC). A.Z. would like to thank the Centre de Recherches Math´ematiques (CRM) for its hospitality	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Bispectrality of the Complementary Bannai-Ito Polynomials	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA