Maximal rigid representations of continuous quivers of type $A$

TL;DR

This paper extends the classification of maximal rigid representations from discrete type $A$ quivers to continuous quivers of the same type, providing a formula for counting isomorphism classes.

Contribution

It introduces a formula for counting maximal rigid representations of continuous type $A$ quivers, generalizing previous discrete quiver results.

Findings

Derived a counting formula for isomorphism classes

Extended classification to continuous quivers

Bridged discrete and continuous quiver representations

Abstract

Bongartz and Gabriel gave a classification of maximal rigid representations for quivers of type $A$ with linear orientation and counted the number of isomorphism classes. In this paper, we give a formula on the number of isomorphism classes of a kind of maximal rigid representations for continuous quivers of type $A$ introduced by Igusa, Rock and Todorov.