Maximal rigid representations of continuous quivers of type $A$

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.