Decomposition of Marsden-Weinstein reductions for representations of quivers

TL;DR

This paper decomposes Marsden-Weinstein reductions for quiver representations into symmetric products of deformations of Kleinian singularities, establishing their irreducibility and providing a detailed structural understanding.

Contribution

It introduces a novel decomposition of Marsden-Weinstein reductions involving symmetric products and deformations, advancing the understanding of their geometric structure.

Findings

Marsden-Weinstein reductions decompose into symmetric products of deformations

The reductions are shown to be irreducible varieties

Provides new structural insights into quiver representation moduli

Abstract

We decompose the Marsden-Weinstein reductions for the moment map associated to representations of a quiver. The decomposition involves symmetric products of deformations of Kleinian singularities, as well as other terms. As a corollary we deduce that the Marsden-Weinstein reductions are irreducible varieties.