A remark on deformations of Hurwitz Frobenius manifolds

TL;DR

This paper explores how multi-KP hierarchies can describe infinitesimal deformations of Hurwitz Frobenius manifolds, linking Shramchenko's deformations to Givental-van de Leur loop group actions.

Contribution

It provides a general formalism for deformations of Frobenius manifolds using multi-KP hierarchies and connects specific deformations to loop group actions.

Findings

Formulas for infinitesimal deformations of Darboux-Egoroff systems

Connection of Shramchenko's deformations to Givental-van de Leur formalism

Enhanced understanding of Frobenius manifold deformations

Abstract

In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold structures on Hurwitz spaces fit into the general formalism of Givental-van de Leur twisted loop group action on the space of semi-simple Frobenius manifolds.