HEUN EQUATIONS AND QUASI EXACT SOLVABILITY

We consider the Heun equations in the context of the quasi-exactly-sol vable spectral problems and establish the conditions for this class of equations to admit algebraic solutions. The Schrodinger operators tha t can be associated with Heun equations are constructed explicitly; in some cases, we present their supersymmetric partners. We study a Heun -like system of equations which is relevant for the classical solution of the two-dimensional Abelian-Higgs model.