Abstract
We apply the method of iterated inflations to show that the wreath product of a cellular algebra with a symmetric group is cellular, and obtain descriptions of the cell and simple modules together with a semisimplicity condition for such wreath products.
Highlights
The wreath product G Sn of a finite group G with a symmetric group Sn is a natural group-theoretic construction with many applications
Wreath products Sm Sn of two symmetric groups are of great importance in the representation theory of the symmetric group
We shall prove that A Sn is cellular for any cellular algebra A, by exhibiting it as an iterated inflation of tensor products of group algebras of symmetric groups
Summary
The wreath product G Sn of a finite group G with a symmetric group Sn is a natural group-theoretic construction with many applications. We shall obtain a convenient graphical description of a well-known method of constructing A Sn modules (section 3), and in section 5 we bring this description together with the cellularity result to deliver results on the representation theory of A Sn, in particular a description of the simple modules and a semisimplicity condition. These results require no extra assumptions on the field (e.g. algebraic closedness)
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