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Bispectrality of the Complementary Bannai-Ito Polynomials
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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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Bispectrality of the Complementary Bannai-Ito Polynomials
Інший ID:
2010 Mathematics Subject Classification: 33C02; 16G02
DOI: http://dx.doi.org/10.3842/SIGMA.2013.018
DOI: http://dx.doi.org/10.3842/SIGMA.2013.018
Посилання:
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.
Підтримка:
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
Дата:
2013
Переглядів:
595
Завантажень:
241
Анотація:
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.
