The q‐Bannai–Ito algebra and multivariate (−q)‐Racah and Bannai–Ito polynomials

Autor: Hadewijch De Clercq, Hendrik De Bie
Jazyk: angličtina
Rok vydání: 2021
Předmět:
33C50
Rank (linear algebra)
33D50
39A13
General Mathematics
SYMMETRY
FOS: Physical sciences
Askey–Wilson polynomials
01 natural sciences
81R50 (primary)
Orthogonality
Askey scheme
ASKEY-WILSON POLYNOMIALS
SYSTEMS
Mathematics - Quantum Algebra
0103 physical sciences
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Bannai–Ito algebra
Quantum Algebra (math.QA)
0101 mathematics
Connection (algebraic framework)
Algebraic number
Abelian group
Mathematical Physics
multivariate polynomials
Askey–Wilson algebra
Mathematics
33C50
33D45
33D50
33D80
39A13
81R50
bispectrality
OPERATORS
Conjecture
q-Racah polynomials
010102 general mathematics
33D80
Mathematical Physics (math-ph)
Algebra
Mathematics and Statistics
Mathematics - Classical Analysis and ODEs
Orthogonal polynomials
Bannai–Ito polynomials
010307 mathematical physics
33D45 (secondary)
Realization (systems)
QUANTUM
COEFFICIENTS
Zdroj: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
ISSN: 1577-1598
0024-6107
1469-7750
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 $\mathcal{A}_n$.
61 pages, added more details on construction of bases in section 2.3 and 2.4, various other small changes
Databáze: OpenAIRE
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