A slice theorem for quivers with an involution

TL;DR

This paper extends the Luna slice theorem to quivers with involution, introducing a local quiver setting analogue to analyze simple supermixed representations and their dimension vectors.

Contribution

It develops a new framework for quivers with involution, enabling the determination of dimension vectors of simple supermixed representations.

Findings

Constructed an analogue to local quiver settings for supermixed quivers.

Determined dimension vectors of simple supermixed representations.

Extended Luna slice theorem to quivers with involution.

Abstract

We study the Luna slice theorem in the case of quivers with an involution or supermixed quivers as introduced by Zubkov. We construct an analogue to the notion of a local quiver setting. We use this technique to determine dimension vectors of simple supermixed representations.