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