Enhanced Nilpotent Representations of a Cyclic Quiver

TL;DR

This paper introduces enhanced nilpotent quiver representations, generalizing existing concepts, and provides a combinatorial parametrization and dimension formula for their orbits under a group action.

Contribution

It defines a new class of enhanced nilpotent quiver representations and develops a combinatorial framework to classify and compute orbit dimensions.

Findings

Finitely many orbits under the group action.

A combinatorial parametrization of orbits.

A formula for orbit dimensions.

Abstract

We define a set of "enhanced" nilpotent quiver representations that generalizes the enhanced nilpotent cone. This set admits an action by an associated algebraic group $K$ with finitely many orbits. We define a combinatorial set that parametrizes the set of orbits under this action and we derive a purely combinatorial formula for the dimension of an orbit.