On $\tau$-tilting finiteness of blocks of Schur algebras

TL;DR

This paper classifies which blocks of classical Schur algebras are $ au$-tilting finite, providing a complete classification for all Schur algebras and specifically for blocks of $S(2,r)$, advancing understanding in representation theory.

Contribution

It offers the first complete classification of $ au$-tilting finite Schur algebras and their blocks, refining previous partial results and focusing on the case of $S(2,r)$.

Findings

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

Identification of $ au$-tilting finiteness for specific blocks.

Refinement of classification for blocks of $S(2,r)$).

Abstract

In this paper, we determine the $\tau$-tilting finiteness for some blocks of (classical) Schur algebras. Combining with the results in arXiv:2010.05206, we get a complete classification of $\tau$-tilting finite Schur algebras. As a refinement, we also give a complete classification of $\tau$-tilting finite blocks of the Schur algebra $S(2,r)$.