The 2-Kronecker Quiver and Systems of Linear Differential Equations

Abstract

We present a way of classifying all the indecomposable representations of the 2-Kronecker quiver over an algebraically closed field. We do this mainly by constructing classes of irregular indecomposable representations by the coxeter functor, and by constructing a class of regular indecomposable representations by mathematical induction using projective resolutions and the Ext^1(A,B) functor.