Weak orders on symmetric groups and posets of support $\tau$-tilting modules

TL;DR

This paper characterizes when the support τ-tilting poset of a finite-dimensional algebra matches the weak order on symmetric groups, revealing infinitely many such algebras.

Contribution

It provides a necessary and sufficient condition for this isomorphism and shows the abundance of such algebras.

Findings

Characterization of when support τ-tilting posets are isomorphic to symmetric group weak order

Existence of infinitely many finite-dimensional algebras with this property

Establishment of a clear criterion for poset isomorphism

Abstract

We give a necessary and sufficient condition for that the support $\tau$-tilting poset of a finite dimensional algebra is isomorphic to the poset of symmetric group with weak order. Moreover we show that there are infinitely many finite dimensional algebras whose support $\tau$-tilting posets are isomorphic to the poset of symmetric group with weak order.