A geometric construction of solutions of the strict dKP(Λ₀) hierarchy

In a previous paper we associated to each invertible constant pseudo difference operator Λ₀ of degree one, two integrable hierarchies in the algebra of pseudo difference operators PsΔ the so-called dKP(Λ₀) hierarchy and its strict version. We show here first that both hierarchies can be described as the compatibility conditions for a proper linearization. Next we present a geometric framework for the construction of solutions of the hierarchies, i.e. we associate to each hierarchy an infinite dimensional variety such that to each point of the variety one can construct a solution of the corresponding hierarchy. This yields a Segal–Wilson type framework for all these integrable hierarchies.