Crampe, Nicolas; Frappat, Luc; Gaboriaud, Julien; Ragoucy, Eric; Vinet, Luc; Zaimi, Meri Griffiths polynomials of Racah type. arXiv:2403.12148 Preprint, arXiv:2403.12148 [math-ph] (2024). MSC: 33C80 33C45 16G60 BibTeX Cite \textit{N. Crampe} et al., ``Griffiths polynomials of Racah type'', Preprint, arXiv:2403.12148 [math-ph] (2024) Full Text: arXiv OA License
Crampé, Nicolas; Gaboriaud, Julien; Poulain d’Andecy, Loïc; Vinet, Luc Matrix elements of \(SO(3)\) in \(sl_3\) representations as bispectral multivariate functions. (English) Zbl 07774846 J. Math. Phys. 64, No. 11, Article ID 111702, 16 p. (2023). MSC: 33C80 81R12 33D45 81R05 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Math. Phys. 64, No. 11, Article ID 111702, 16 p. (2023; Zbl 07774846) Full Text: DOI arXiv
Crampe, N.; Frappat, L.; Gaboriaud, J.; Ragoucy, E.; Vinet, L.; Zaimi, M. \(\lambda\)-Griffiths polynomials: Bispectrality and biorthogonality. arXiv:2311.03256 Preprint, arXiv:2311.03256 [math-ph] (2023). BibTeX Cite \textit{N. Crampe} et al., ``$\lambda$-Griffiths polynomials: Bispectrality and biorthogonality'', Preprint, arXiv:2311.03256 [math-ph] (2023) Full Text: arXiv OA License
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei The rational Sklyanin algebra and the Wilson and para-Racah polynomials. (English) Zbl 1508.17016 J. Math. Phys. 63, No. 6, Article ID 061704, 14 p. (2022). MSC: 17B37 33C45 33C47 33C80 PDFBibTeX XMLCite \textit{G. Bergeron} et al., J. Math. Phys. 63, No. 6, Article ID 061704, 14 p. (2022; Zbl 1508.17016) Full Text: DOI arXiv
Bussière, Ismaël; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei Bispectrality and biorthogonality of the rational functions of \(q\)-Hahn type. (English) Zbl 1519.33012 J. Math. Anal. Appl. 516, No. 1, Article ID 126443, 17 p. (2022). MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{I. Bussière} et al., J. Math. Anal. Appl. 516, No. 1, Article ID 126443, 17 p. (2022; Zbl 1519.33012) Full Text: DOI arXiv
Crampé, Nicolas; Gaboriaud, Julien; d’Andecy, Loïc Poulain; Vinet, Luc Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series. (English) Zbl 1504.17017 Ann. Henri Poincaré 23, No. 7, 2657-2682 (2022). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B35 16S30 81R05 PDFBibTeX XMLCite \textit{N. Crampé} et al., Ann. Henri Poincaré 23, No. 7, 2657--2682 (2022; Zbl 1504.17017) Full Text: DOI arXiv
Beaudoin, André; Bergeron, Geoffroy; Brillant, Antoine; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei Orthogonal polynomials and the deformed Jordan plane. (English) Zbl 1491.33009 J. Math. Anal. Appl. 507, No. 1, Article ID 125717, 10 p. (2022). MSC: 33C47 PDFBibTeX XMLCite \textit{A. Beaudoin} et al., J. Math. Anal. Appl. 507, No. 1, Article ID 125717, 10 p. (2022; Zbl 1491.33009) Full Text: DOI arXiv
Crampé, Nicolas; Frappat, Luc; Gaboriaud, Julien; Poulain d’Andecy, Loïc; Ragoucy, Eric; Vinet, Luc The Askey-Wilson algebra and its avatars. (English) Zbl 1519.81276 J. Phys. A, Math. Theor. 54, No. 6, Article ID 063001, 32 p. (2021). MSC: 81R05 33D45 17B37 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Phys. A, Math. Theor. 54, No. 6, Article ID 063001, 32 p. (2021; Zbl 1519.81276) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane Howe duality and algebras of the Askey-Wilson type: an overview. (English) Zbl 1492.17015 Paranjape, M. B. (ed.) et al., Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1–5, 2019. Cham: Springer. CRM Ser. Math. Phys., 225-233 (2021). Reviewer: Dwight Williams II (New York) MSC: 17B37 16T20 17A45 17A70 33C52 81R05 33D45 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., in: Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1--5, 2019. Cham: Springer. 225--233 (2021; Zbl 1492.17015) Full Text: DOI arXiv
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei Sklyanin-like algebras for \((q\)-)linear grids and \((q\)-)para-Krawtchouk polynomials. (English) Zbl 1456.81265 J. Math. Phys. 62, No. 1, Article ID 013505, 20 p. (2021). MSC: 81R50 17B37 47B40 33D45 PDFBibTeX XMLCite \textit{G. Bergeron} et al., J. Math. Phys. 62, No. 1, Article ID 013505, 20 p. (2021; Zbl 1456.81265) Full Text: DOI arXiv
Gaboriaud, Julien; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Degenerate Sklyanin algebras, Askey-Wilson polynomials and Heun operators. (English) Zbl 1519.81279 J. Phys. A, Math. Theor. 53, No. 44, Article ID 445204, 19 p. (2020). MSC: 81R05 33D45 14A22 16S38 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 53, No. 44, Article ID 445204, 19 p. (2020; Zbl 1519.81279) Full Text: DOI arXiv
Crampé, Nicolas; Gaboriaud, Julien; Vinet, Luc; Zaimi, Meri Revisiting the Askey-Wilson algebra with the universal \(R\)-matrix of \(U_q(\mathfrak{sl}_2)\). (English) Zbl 1511.17029 J. Phys. A, Math. Theor. 53, No. 5, Article ID 05LT01, 10 p. (2020). MSC: 17B37 17B10 81R50 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Phys. A, Math. Theor. 53, No. 5, Article ID 05LT01, 10 p. (2020; Zbl 1511.17029) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc A Howe correspondence for the algebra of the \(\mathfrak{osp}(1 | 2)\) Clebsch-Gordan coefficients. (English) Zbl 1448.81357 Phys. Lett., A 384, No. 29, Article ID 126746, 8 p. (2020). MSC: 81R10 81R15 PDFBibTeX XMLCite \textit{J. Gaboriaud} and \textit{L. Vinet}, Phys. Lett., A 384, No. 29, Article ID 126746, 8 p. (2020; Zbl 1448.81357) Full Text: DOI arXiv
Frappat, Luc; Gaboriaud, Julien; Ragoucy, Eric; Vinet, Luc The dual pair \((U_q(\mathfrak{s} \mathfrak{u}(1, 1)), \mathfrak{o}_{q^{1 / 2}}(2 n)),q\)-oscillators, and Askey-Wilson algebras. (English) Zbl 1443.81042 J. Math. Phys. 61, No. 4, 041701, 11 p. (2020). MSC: 81R50 33D45 22E70 81T55 81R05 PDFBibTeX XMLCite \textit{L. Frappat} et al., J. Math. Phys. 61, No. 4, 041701, 11 p. (2020; Zbl 1443.81042) Full Text: DOI arXiv
Bernard, Pierre-Antoine; Gaboriaud, Julien; Vinet, Luc Superintegrability and the dual \(- 1\) Hahn algebra in superconformal quantum mechanics. (English) Zbl 1435.81099 Ann. Phys. 418, Article ID 168171, 21 p. (2020). MSC: 81R50 17B37 17B81 PDFBibTeX XMLCite \textit{P.-A. Bernard} et al., Ann. Phys. 418, Article ID 168171, 21 p. (2020; Zbl 1435.81099) Full Text: DOI arXiv
Frappat, Luc; Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei The Higgs and Hahn algebras from a Howe duality perspective. (English) Zbl 1476.81035 Phys. Lett., A 383, No. 14, 1531-1535 (2019). MSC: 81Q05 81Q35 42C05 14M27 37K10 PDFBibTeX XMLCite \textit{L. Frappat} et al., Phys. Lett., A 383, No. 14, 1531--1535 (2019; Zbl 1476.81035) Full Text: DOI arXiv
Frappat, Luc; Gaboriaud, Julien; Ragoucy, Eric; Vinet, Luc The \(q\)-Higgs and Askey-Wilson algebras. (English) Zbl 1430.81042 Nucl. Phys., B 944, Article ID 114632, 13 p. (2019). MSC: 81R50 17B37 17B35 33D45 81Q35 81R05 PDFBibTeX XMLCite \textit{L. Frappat} et al., Nucl. Phys., B 944, Article ID 114632, 13 p. (2019; Zbl 1430.81042) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei The Racah algebra as a commutant and Howe duality. (English) Zbl 1411.81112 J. Phys. A, Math. Theor. 51, No. 50, Article ID 50LT01, 8 p. (2018). MSC: 81R12 33C45 17B67 22E70 37K10 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 51, No. 50, Article ID 50LT01, 8 p. (2018; Zbl 1411.81112) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra. (English) Zbl 1402.81132 Nucl. Phys., B 937, 226-239 (2018). MSC: 81Q05 17A70 17B81 22E70 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., Nucl. Phys., B 937, 226--239 (2018; Zbl 1402.81132) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc An algebraic interpretation of the \(q\)-Meixner polynomials. (English) Zbl 1390.33034 Ramanujan J. 46, No. 1, 127-149 (2018). MSC: 33D45 81R50 PDFBibTeX XMLCite \textit{J. Gaboriaud} and \textit{L. Vinet}, Ramanujan J. 46, No. 1, 127--149 (2018; Zbl 1390.33034) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei The generalized Racah algebra as a commutant. arXiv:1808.09518 Preprint, arXiv:1808.09518 [math-ph] (2018). MSC: 20C35 22E70 81R12 BibTeX Cite \textit{J. Gaboriaud} et al., ``The generalized Racah algebra as a commutant'', Preprint, arXiv:1808.09518 [math-ph] (2018) Full Text: DOI arXiv OA License
Gaboriaud, Julien; Genest, Vincent X.; Lemieux, Jessica; Vinet, Luc A superintegrable discrete oscillator and two-variable Meixner polynomials. (English) Zbl 1326.81090 J. Phys. A, Math. Theor. 48, No. 41, Article ID 415202, 14 p. (2015). MSC: 81Q80 33C80 39A14 33C50 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 48, No. 41, Article ID 415202, 14 p. (2015; Zbl 1326.81090) Full Text: DOI arXiv