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<p>We study certain overlap coefficients appearing in representation theory of the quantum algebra <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {U}_q(\mathfrak {sl}_2(\mathbb {C}))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">U</mi> <mi>q</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="fraktur">sl</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. The overlap coefficients can be identified as products of Askey–Wilson functions, leading to an algebraic interpretation of the multivariate Askey–Wilson functions introduced by Geronimo and Iliev [<CitationRef CitationID="CR1">1</CitationRef>]. We use the underlying coalgebra structure to derive <i>q</i>-difference equations satisfied by the multivariate Askey–Wilson functions.</p>

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Multivariate Askey–Wilson functions and overlap coefficients

  • 期刊论文

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  • 发表日期：

    2025年10月29日

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  • Wolter Groenevelt

摘要

We study certain overlap coefficients appearing in representation theory of the quantum algebra \(\mathcal {U}_q(\mathfrak {sl}_2(\mathbb {C}))\) U q ( sl 2 ( C ) ) . The overlap coefficients can be identified as products of Askey–Wilson functions, leading to an algebraic interpretation of the multivariate Askey–Wilson functions introduced by Geronimo and Iliev [1]. We use the underlying coalgebra structure to derive q-difference equations satisfied by the multivariate Askey–Wilson functions.