Calogero-Moser hierarchy and KP hierarchy

TL;DR

This paper establishes a connection between the solution spaces of the rational Calogero-Moser hierarchy and a specific class of KP hierarchy solutions, extending previous mathematical results.

Contribution

It generalizes earlier work by explicitly identifying the solution spaces of these two hierarchies, linking rational Calogero-Moser solutions with polynomial tau functions in the KP hierarchy.

Findings

Identified the solution space of the rational Calogero-Moser hierarchy.

Connected these solutions to KP hierarchy solutions with polynomial tau functions.

Extended previous results by Airault-McKean-Moser and Krichever.

Abstract

The space of solutions of the rational Calogero-Moser hierarchy, and the space of solutions of the KP hierarchy whose tau functions are monic polynomials in $t_1$ with coefficients depending on $t_n$, $n > 1$, are identified, generalizing earlier results of Airault-McKean-Moser and Krichever.