Finiteness conditions for Borel--Schur algebras

Abstract

We classify the $\tau$-tilting finite, silting-discrete, and derived-discrete Borel--Schur algebras over an algebraically closed field of arbitrary characteristic. We further prove that derived-discreteness is equivalent to silting-discreteness within this family and determine precisely when these equivalent conditions are strictly stronger than $\tau$-tilting finiteness.

29 pages. Substantially revised version. In addition to the classification of $\tau$-tilting finite Borel--Schur algebras, we now classify the silting-discrete and derived-discrete cases