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

摘要

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