The cellular structure of wreath product algebras

We review the definitions and basic theory of cellular algebras as

developed in the papers of Graham and Lehrer and of K ?

onig and Xi.

We then introduce a reformulation of the concept of an iterated inflation

of cellular algebras (a concept due originally to K ?onig and Xi), which

we use to show that the Brauer algebra is cellular (following the work

of K ?onig and Xi). We then review the notion of the wreath product of

an algebra with a symmetric group, and apply our work on iterated

inflations to prove that the wreath product of a cellular algebra with a

symmetric group is in all cases cellular, and we obtain a description of

the cell modules of such a wreath product.