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Bethe ansatz diagonalization of the Heun–Racah operator

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Abstract

The diagonalization of the Heun–Racah operator is studied with the help of the modified algebraic Bethe ansatz. This operator is the most general bilinear expression in two generators of the Racah algebra. A presentation of this algebra is given in terms of dynamical operators and allows the construction of Bethe vectors for the Heun–Racah operator. The associated Bethe equations are derived for both the homogeneous and inhomogeneous cases.

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Acknowledgements

PAB holds an Alexander-Graham-Bell scholarship from the Natural Sciences and Engineering Research Council of Canada (NSERC). GC thanks the Department of Physics of the Université de Montréal for partial support. NC thanks the CRM for its hospitality and are supported by the international research project AAPT of the CNRS and the ANR Project AHA ANR-18-CE40-0001. The research of LV is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, QC, H3C 3J7, Canada

    Pierre-Antoine Bernard, Gauvain Carcone & Luc Vinet

  2. Institut Denis-Poisson CNRS/UMR 7013, Université de Tours, Université d’Orléans, Parc de Grandmont, 37200, Tours, France

    Nicolas Crampé

  3. IVADO, Montréal, QC, H2S 3H1, Canada

    Luc Vinet

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  1. Pierre-Antoine Bernard
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Correspondence to Nicolas Crampé.

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Bernard, PA., Carcone, G., Crampé, N. et al. Bethe ansatz diagonalization of the Heun–Racah operator. Lett Math Phys 113, 8 (2023). https://doi.org/10.1007/s11005-023-01633-7

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