On $\tau$-tilting finiteness of the Schur algebra

TL;DR

This paper classifies when Schur algebras are $ au$-tilting finite over algebraically closed fields, covering most cases except a few small ones, thus advancing understanding of their representation theory.

Contribution

It provides a comprehensive determination of $ au$-tilting finiteness for Schur algebras across various characteristics, filling gaps in existing knowledge.

Findings

Most Schur algebras are $ au$-tilting finite.

Identifies specific small cases where finiteness does not hold.

Advances the classification in representation theory of Schur algebras.

Abstract

We determined the $\tau$-tilting finiteness of Schur algebras over an algebraically closed field of arbitrary characteristic, except for a few small cases.