On an algebro-geometric discretization of KP hierarchy

TL;DR

This paper investigates a specific algebro-geometric discretization of the KP hierarchy, demonstrating its invertibility and deriving explicit flow equations, with future work planned on its Hamiltonian structure.

Contribution

It proves the generic invertibility of Gieseker's algebro-geometric discretization of the KP hierarchy and provides explicit formulas for the flow equations.

Findings

Discretization is generically invertible

Explicit flow equations are derived

Foundation laid for Hamiltonian analysis

Abstract

This paper studies a certain completely integrable discretization of the KP hierarchy. This was constructed by Gieseker in \cite{Gie1}, from certain algebro-geometric data. This paper has the dual aim of showing that this construction is generically invertible, and obtaining explicit expressions for the flow equations. A subsequent article will discuss the Hamiltonian structure of this system.