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

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.