Geodesic
Tree Normal Forms for Quiver Representations
Documenta mathematica, Tome 24 (2019), pp. 1245-1294.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 16G20
Keywords: quiver representations, tree modules, moduli spaces, normal forms, cell decompositions 
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     author = {Kinser, Ryan and Weist, Thorsten},
     title = {Tree {Normal} {Forms} for {Quiver} {Representations}},
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Kinser, Ryan; Weist, Thorsten. Tree Normal Forms for Quiver Representations. Documenta mathematica, Tome 24 (2019), pp. 1245-1294. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a31/