Applications of loop groups and standard modules to Jacobians and theta functions of isospectral curves

Abstract

Let L(z) be an element of M n {€, [z,z~1]). In this work we study the structure of isospectral curves given by /(z, λ) = 0, f(z,\) -det(L(z) -λ), their Jacobians and the relationship between standard modules and the corresponding theta functions. We assume that /(z, λ) is irreducible and nonsingular for /(z,λ) = 0 and z G C\ The element L(z) will be called good, if the centralizers Introduction.