Cell algebra structure on generalized Schur algebras

TL;DR

This paper establishes a cell algebra structure on certain generalized Schur algebras, enabling the construction of irreducible representations and the determination of their quasi-hereditary property.

Contribution

It introduces a new cell algebra framework for generalized Schur algebras, facilitating representation theory analysis.

Findings

Cell algebra structure successfully constructed for the algebras.

Irreducible representations explicitly constructed.

Criteria for quasi-hereditary property determined.

Abstract

A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the algebras are quasi-hereditary.