The $q$-Bannai-Ito algebra and multivariate $(-q)$-Racah and Bannai-Ito polynomials
| Autor: | De Bie, Hendrik, De Clercq, Hadewijch |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jlms.12367 |
| Popis: | The Gasper and Rahman multivariate $(-q)$-Racah polynomials appear as connection coefficients between bases diagonalizing different abelian subalgebras of the recently defined higher rank $q$-Bannai-Ito algebra $\mathcal{A}_n^q$. Lifting the action of the algebra to the connection coefficients, we find a realization of $\mathcal{A}_n^q$ by means of difference operators. This provides an algebraic interpretation for the bispectrality of the multivariate $(-q)$-Racah polynomials, as was established in [Iliev, Trans. Amer. Math. Soc. 363 (3) (2011), 1577-1598]. Furthermore, we extend the Bannai-Ito orthogonal polynomials to multiple variables and use these to express the connection coefficients for the $q = 1$ higher rank Bannai-Ito algebra $\mathcal{A}_n$, thereby proving a conjecture from [De Bie et al., Adv. Math. 303 (2016), 390-414]. We derive the orthogonality relation of these multivariate Bannai-Ito polynomials and provide a discrete realization for $\mathcal{A}_n$. Comment: 61 pages, added more details on construction of bases in section 2.3 and 2.4, various other small changes |
| Databáze: | arXiv |
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