A Reciprocity Result for Projective Indecomposable Modules of Cellular Algebras and BGG Algebras

TL;DR

This paper extends Landrock's Lemma to cellular and BGG algebras, revealing that BGG reciprocity aligns with Loewy structure due to duality between injective and projective modules.

Contribution

It adapts Landrock's Lemma for symmetric algebras to cellular and BGG algebras, establishing a new relation between radical layers of projective modules.

Findings

Landrock's Lemma applies to cellular and BGG algebras

BGG reciprocity respects Loewy structure

Duality between injective hulls and projective covers is key

Abstract

We show that an adaptation of Landrock's Lemma for symmetric algebras also holds for cellular algebras and BGG algebras. This is a result relating the radical layers of any two projective modules. The reason it holds in our setting is that there is a duality between injective hulls and projective covers. As a corollary we deduce that BGG reciprocity respects Loewy structure.