Solutions of the Yang equation with rational irreducible spectral curves

The author studies rank 1 solutions of the Yang equation $\mathscr R^{12}\mathscr L^{13}\mathscr L^{'23}=\mathscr L^{'23}\mathscr L^{13}\mathscr R^{12}$ with rational irreducible spectral curves with ordinary double points. A complete list of the solutions is given, and it is shown that these solutions, which satisfy the Yang–Baxter equation, lead to the $R$-matrix of Cherednik.