On $\tau$-tilting finite Borel-Schur algebras

TL;DR

This paper classifies when Borel-Schur algebras are $ au$-tilting finite by applying advanced silting theory techniques, including sign decomposition and silting quiver symmetry, and explores new properties of these algebras.

Contribution

It provides a complete characterization of $ au$-tilting finiteness for Borel-Schur algebras using novel methods in silting theory.

Findings

Complete classification of $ au$-tilting finite Borel-Schur algebras

Application of sign decomposition and silting quiver symmetry techniques

Discovery of new properties related to Borel-Schur algebras and sign decomposition

Abstract

We completely determine the $\tau$-tilting finiteness of Borel-Schur algebras. To achieve this, we use two recently introduced techniques in silting theory: sign decomposition as introduced by Aoki, Higashitani, Iyama, Kase and Mizuno [arXiv:2203.15213], and symmetry of silting quivers as investigated by Aihara and the author [arXiv:2205.00472]. Besides, we explore some new properties for both Borel-Schur algebra and sign decomposition.