Logo image
TREE NORMAL FORMS FOR QUIVER REPRESENTATIONS
Journal article   Peer reviewed

TREE NORMAL FORMS FOR QUIVER REPRESENTATIONS

Ryan Kinser and Thorsten Weist
Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung., Vol.24, pp.1245-1294
01/01/2019
DOI: 10.25537/dm.2019v24.1245-1294
url
https://arxiv.org/pdf/1810.04977View
Open Access

Abstract

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 Physical Sciences Science & Technology

Details

Metrics

18 Record Views
Logo image