Kinser, Ryan; Weist, Thorsten

Tree Normal Forms for Quiver Representations

Doc. Math. 24, 1245-1294 (2019)
DOI: 10.25537/dm.2019v24.1245-1294
Communicated by Henning Krause


We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables of smaller dimension vector. This is then specialized to the situation of tree modules, where the existence of a special basis simplifies computations and gives nicer normal forms. Motivated by a conjecture of Kac, we use this to construct cells of indecomposable representations as deformations of tree modules. The second part of the paper develops geometric tools for constructing cells of indecomposable representations from torus actions on moduli spaces of representations. As an application, we combine these methods to construct families of indecomposables grouped into cells. These actually give a normal form for all indecomposables of certain roots.

Mathematics Subject Classification



quiver representations, tree modules, moduli spaces, normal forms, cell decompositions


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Kinser, Ryan
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA
Weist, Thorsten
Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42097 Wuppertal, Germany