Supersymmetric Extension of the Kadomtsev–Petviashvili Hierarchy and the Universal Super Grassmann Manifold

Abstract

A supersymmetric extension of the Kadomtsev–Petviashvili hierarchy (SKP hierarchy) is proposed. It is shown that the solution space is identical with the universal super Grassmann manifold. An explicit formula of a solution to the SKP hierarchy is presented as a quotient of superdeterminants. Our arguments are based upon algebraic investigations of the structure of a linear supersymmetric differential equation.