The Tamari lattice as it arises in quiver representations

TL;DR

This paper explores how the Tamari lattice naturally appears within the representation theory of quivers, specifically as the poset of torsion classes ordered by inclusion for a directed path quiver.

Contribution

It establishes a novel connection between Tamari lattices and the structure of torsion classes in quiver representation theory.

Findings

Tamari lattice corresponds to torsion classes in a directed path quiver

The poset of torsion classes forms a Tamari lattice

Provides new insights into the combinatorial structure of quiver representations

Abstract

In this paper, we explain how the Tamari lattice arises in the context of the representation theory of quivers, as the poset whose elements are the torsion classes of a directed path quiver, with the order relation given by inclusion.