Torsion classes realize the Tamari lattice in type A

The protagonist of this talk will be the oriented quiver of Dynkin type A. We will introduce its (finitely many) indecomposable representations, use them to classify all quotient-closed subcategories of rep \(A_n\), and discover which among these constitute torsion classes via “bracket vectors”. The torsion classes ordered by inclusion recover the Tamari lattice, a beloved combinatorial lattice encoding a variety of known objects. This talk follows the paper “The Tamari lattice as it arises in quiver representations” by Hugh Thomas.

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Date published: Wednesday, February 11, 2026