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.
CITATION STYLE
Barnard, E., Gunawan, E., Meehan, E., & Schiffler, R. (2023). Cambrian combinatorics on quiver representations (type A). Advances in Applied Mathematics, 143. https://doi.org/10.1016/j.aam.2022.102428
Mendeley helps you to discover research relevant for your work.