Cambrian combinatorics on quiver representations (type A)
Representation Theory
2022-10-11 v4 Combinatorics
Rings and Algebras
Abstract
This paper presents a geometric model of the Auslander-Reiten quiver of a type A quiver together with a stability function for which all indecomposable modules are stable. We also introduce a new Catalan object which we call a maximal almost rigid representation. We show that its endomorphism algebra is a tilted algebra of type A. We define a partial order on the set of maximal almost rigid representations and use our new geometric model to show that this partial order is a Cambrian lattice.
Cite
@article{arxiv.1912.02840,
title = {Cambrian combinatorics on quiver representations (type A)},
author = {Emily Barnard and Emily Gunawan and Emily Meehan and Ralf Schiffler},
journal= {arXiv preprint arXiv:1912.02840},
year = {2022}
}
Comments
28 pages, 16 figures. Comments are welcome