On Auslander-Reiten sequences for Borel-Schur algebras

TL;DR

This paper classifies Borel-Schur algebras with finite representation type and determines Auslander-Reiten sequences for many simple modules, providing insights into their module structure and socles.

Contribution

It offers a classification of finite type Borel-Schur algebras and explicitly describes Auslander-Reiten sequences for a broad class of simple modules.

Findings

Identification of finite representation type Borel-Schur algebras

Explicit Auslander-Reiten sequences for simple modules

Partial description of socle structures

Abstract

We classify Borel-Schur algebras having finite representation type. We also de- termine Auslander-Reiten sequences for a large class of simple modules over Borel- Schur algebras. A partial information on the structure of the socles of Borel-Schur algebras is given.