Group actions on quiver varieties and applications

TL;DR

This paper investigates how finite groups act on quiver varieties, decomposes the fixed points using cohomology, and constructs branes in hyperkähler quiver varieties as fixed loci of these actions.

Contribution

It introduces a method to analyze group actions on quiver varieties and provides a modular interpretation of fixed loci, leading to new constructions of branes in hyperkähler geometry.

Findings

Decomposition of fixed loci via group cohomology

Modular interpretation of fixed components

Construction of branes in hyperkähler quiver varieties

Abstract

We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a modular interpretation of each component. As an application, we construct branes in hyperkaehler quiver varieties, as fixed loci of such actions.