Moduli spaces of meromorphic connections, quiver varieties, and integrable deformations

TL;DR

This paper reviews symmetries of moduli spaces of meromorphic connections on the Riemann sphere, explores their integrable deformations, and demonstrates their realization as quiver varieties, highlighting their structural properties.

Contribution

It provides a new perspective by realizing moduli spaces as quiver varieties and analyzing their symmetries and integrable deformations.

Findings

Symmetries of moduli spaces are characterized.

Realization of moduli spaces as quiver varieties is established.

Symmetries of integrable deformations are discussed.

Abstract

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the study of the symmetries, a realization of the moduli spaces as quiver varieties is given and plays an essential role.