On equivariant bundles and their moduli spaces

TL;DR

This paper studies $( ext{Gamma},G)$-bundles over ramified covers of algebraic curves, providing a new description in terms of $ ext{H}$-bundles on the base, extending previous work by Balaji and Seshadri.

Contribution

It introduces a novel framework to describe $( ext{Gamma},G)$-bundles via $ ext{H}$-bundles, generalizing and clarifying earlier results.

Findings

Provides a description of $( ext{Gamma},G)$-bundles in terms of $ ext{H}$-bundles.

Extends previous work of Balaji and Seshadri.

Clarifies the structure of moduli spaces of equivariant bundles.

Abstract

Let $G$ be an algebraic group and $\Gamma$ a finite subgroup of automorphisms of $G$. Fix also a possibly ramified $\Gamma$-covering $\widetilde{X} \to X$. In this setting one may define the notion of $(\Gamma,G)$-bundles over $\widetilde{X}$ and, in this paper, we give a description of these objects in terms of $\mathcal{H}$-bundles on $X$, for an appropriate group $\mathcal{H}$ over $X$ which depends on the local type of the $(\Gamma,G)$-bundles we intend to parametrize. This extends, and along the way clarifies, an earlier work of Balaji and Seshadri.