Cellularity of generalized Schur algebras via Cauchy decomposition

Abstract

We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This filtration is then used to provide a cellular structure for generalized Schur algebras associated to an arbitrary cellular algebra. Applications to the cellularity of wreath product algebras $A\wr {\mathfrak{S}}_d$ are also considered.