Certain Reductions of Hitchin Systems of Rank 2 and Genera 2 and 3

Abstract—Certain reductions of Hitchin systems of rank 2 and genera 2 and 3 are considered, which are shown to give integrable systems of two (respectively, three) interacting points on the line. It is shown that the reduced systems are particular cases of an integrable system related to the Lagrange interpolation polynomial. The admissibility of the reduction is proved using computer techniques. A reference to published software programs is given in the text.