Bethe ansatz diagonalization of the Heun-Racah operator

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.