The Heun equation and the Calogero-Moser-Sutherland system III: the finite gap property and the monodromy

Abstract

A new approach to the finite-gap property for the Heun equation is constructed. The relationship between the finite-dimensional invariant space and the spectral curve is clarified. The monodromies are calculated and are expressed as hyperelliptic integrals. Applications to the spectral problem for the $B{C}_1$ Inozemtsev model are obtained.

24 pages