Generalized Schur Algebras

TL;DR

This paper introduces and analyzes generalized Schur algebras, providing filtrations that help classify their irreducible representations over various fields, advancing understanding in algebra representation theory.

Contribution

The paper defines and studies generalized Schur algebras, offering new methods to parameterize irreducible representations across different field characteristics.

Findings

Filtrations lead to parameterizations of irreducible representations.

Analysis applies to fields of characteristic 0 and positive characteristic p.

Provides a framework for understanding generalized Schur algebras.

Abstract

Left and right "generalized Schur algebras", previously introduced by the author, are defined and analyzed. Filtrations of these algebras lead, in most cases, to parameterizations of the their irreducible representations over fields of characteristic 0 and fields of positive characteristic p.