Generalised Gabriel-Roiter measure and thin representations
Representation Theory
2024-12-16 v2
Abstract
For Dynkin and Euclidean quivers, it is shown that Gabriel-Roiter measures of thin representations equal the induced chain length functions on the corresponding system of subquivers. This allows a combinatorial procedure to find a GR filtration of thin representations, showing that GR measures of thin representations are field-independent. It is proved that an indecomposable filtration of a thin representation is a GR filtration for a suitable choice of a length function on the category of finite-dimensional representations.
Cite
@article{arxiv.2402.05051,
title = {Generalised Gabriel-Roiter measure and thin representations},
author = {Dominik Krasula},
journal= {arXiv preprint arXiv:2402.05051},
year = {2024}
}