Algebraic solutions of the multicomponent KP hierarchy (Q1589691)

This paper is devoted to a higher rank generalization of the relation between theta functions of Jacobians and the KP hierarchy. More precisely, the well-known relation between the theta function of a Jacobian and the tau function of a certain point of an infinite Grassmannian is generalized for nonlinear theta functions. As a result it is possible to write down tau functions for the \(n\)-congruent KP hierarchy in terms of non-abelian thetas.