Moduli of filtered quiver representations

TL;DR

This paper constructs moduli spaces for filtered quiver representations using ladder quivers and explores associated determinantal theta functions, advancing the understanding of stability conditions and geometric structures in representation theory.

Contribution

It introduces a novel construction of moduli spaces for filtered quiver representations via ladder quivers and analyzes determinantal theta functions on these spaces.

Findings

Construction of moduli spaces for filtered representations

Introduction of ladder quivers for stability analysis

Study of determinantal theta functions on the moduli spaces

Abstract

In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered representations uses the moduli of representations of ladder quiver. The ladder quiver is introduced using a given quiver and a linear type quiver. We also study determinantal theta functions on such moduli spaces.