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Bethe ansatz diagonalization of the Heun-Racah operator

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arxiv 2209.09213 v1 pith:PYSL4MDO submitted 2022-09-19 math-ph math.MP

Pierre-Antoine Bernard , Gauvain Carcone , Nicolas Crampe , Luc Vinet This is my paper · ORCID
classification math-phmath.MP
keywords betheoperatorheun-racahalgebraansatzalgebraicallowsassociated
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The Heun-Racah operator is diagonalized 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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  1. The $q$-Racah polynomials from scalar products of Bethe states II

    math-ph 2025-01 conditional novelty 6.0 of 10

    The paper derives normalized scalar products of on-shell and off-shell Bethe states using Leonard triples, obtains explicit solutions of Belliard-Slavnov systems, and gives a determinant formula for q-Racah polynomials.

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