Journal of Lie Theory 22 (2012), No. 4, 1065--1073
Copyright Heldermann Verlag 2012
A Reciprocity Result for Projective Indecomposable Modules of Cellular Algebras and BGG Algebras
Chris Bowman
Dept. of Pure Mathematics, Corpus Christi College, University of Cambridge, Cambridge CB2 1RH, England
c.bowman@dpmms.cam.ac.uk
Stuart Martin
Dept. of Pure Mathematics, Magdalene College, University of Cambridge, Cambridge CB2 1RH, England
s.martin@dpmms.cam.ac.uk
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. As a corollary we deduce that BGG reciprocity respects Loewy structure.
Keywords: Cellular algebras, BGG algebras, Loewy structure.
MSC: 20C30
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