Cellularity of endomorphism algebras of Young permutation modules

TL;DR

This paper proves that the endomorphism algebra of any Young permutation module is cellular and identifies which among them are quasi-hereditary, advancing understanding of their algebraic structure.

Contribution

It establishes the cellularity of endomorphism algebras of Young permutation modules and characterizes the quasi-hereditary cases, providing new structural insights.

Findings

Endomorphism algebra of any Young permutation module is cellular

Identification of quasi-hereditary cases among these algebras

Enhanced understanding of their algebraic properties

Abstract

It is shown that the endomorphism algebra of an arbitrary Young permutation module is cellular. Those are are quasi-hereditary are then determined.