Bispectrality of the Complementary Bannai-Ito Polynomials
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149225 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719315516588032 |
|---|---|
| author | Genest, V.X. Vinet, L. Zhedanov, A. |
| author_facet | Genest, V.X. Vinet, L. Zhedanov, A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T18:19:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149225 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:19:30Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Genest, V.X. Vinet, L. Zhedanov, A. 2019-02-19T19:01:13Z 2019-02-19T19:01:13Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 33C02; 16G02 DOI: http://dx.doi.org/10.3842/SIGMA.2013.018 https://nasplib.isofts.kiev.ua/handle/123456789/149225 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. 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 en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bispectrality of the Complementary Bannai-Ito Polynomials Article published earlier |
| spellingShingle | Bispectrality of the Complementary Bannai-Ito Polynomials Genest, V.X. Vinet, L. Zhedanov, A. |
| title | Bispectrality of the Complementary Bannai-Ito Polynomials |
| title_full | Bispectrality of the Complementary Bannai-Ito Polynomials |
| title_fullStr | Bispectrality of the Complementary Bannai-Ito Polynomials |
| title_full_unstemmed | Bispectrality of the Complementary Bannai-Ito Polynomials |
| title_short | Bispectrality of the Complementary Bannai-Ito Polynomials |
| title_sort | bispectrality of the complementary bannai-ito polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149225 |
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