Bethe ansatz for the Ruijsenaars model of \(BC_1\)-type (Q2473424)

The author introduces the one-dimensional elliptic Ruijsenaars model of type \(BC_1\), i.e., \[ L=a(z)T^{2\gamma}+b(z)T^{-2\gamma}+c(z), \] where \[ \begin{aligned}&a(z)=\prod_{p=0}^{3} \frac{\sigma_p (z-\mu_p)\sigma_p (z+\gamma-\mu'_p)}{\sigma_p (z) \sigma_p (z+\gamma)},\\ & b(z)=a(-z),\\ & c(z)=\sum_{p=0}^{3}c_p (\zeta_p (z+\gamma)-\zeta_p (z-\gamma)),\\ &\zeta_p (z)=\frac{\sigma'_p (z)}{\sigma_p (z)}=-\eta_p +\zeta(z+\omega_p). \end{aligned} \] He shows that \(L\) has meromorphic eigenfunctions expressed by a variant of Bethe ansatz when all coupling constants of operator \(L\) are integers, and generalizes the Bethe ansatz formulas in the \(A_1\) case.