A new approach to simple modules for preprojective algebras

TL;DR

This paper introduces a novel method for classifying simple modules of deformed preprojective algebras, avoiding complex general position arguments used in previous classifications.

Contribution

It presents a new approach to classify simple modules for deformed preprojective algebras without relying on general position arguments.

Findings

Provides a simplified classification method

Avoids complex geometric arguments

Enhances understanding of module structures

Abstract

The work of the first author on the moment map for representations of quivers included a classification of the possible dimension vectors of simple modules for deformed preprojective algebras. That classification was later used to solve an additive analogue of the Deligne-Simpson problem. The last step in the proof of the classification involved some general position arguments; here we give a new approach which avoids such arguments.