Ringel Duality for Extended ZigZag Schur Algebra

TL;DR

This paper proves that extended zigzag Schur algebras are Ringel self-dual, supporting their conjectured Morita equivalence to RoCK blocks of classical Schur algebras, thus advancing understanding in algebraic representation theory.

Contribution

It establishes the Ringel self-duality of extended zigzag Schur algebras, a key step towards confirming their conjectured Morita equivalence to RoCK blocks.

Findings

Extended zigzag Schur algebras are Ringel self-dual.

Supports conjecture of Morita equivalence to RoCK blocks.

Advances understanding of algebraic structures in representation theory.

Abstract

Extended zigzag Schur algebras are quasi-hereditary algebras which are conjecturally Morita equivalent to RoCK blocks of classical Schur algebras. We prove that extended zigzag Schur algebras are Ringel self-dual.