Wreath Hecke algebras and centralizer construction for wreath products

Generalizing the centralizer construction of Molev and Olshanski on symmetric groups, we study the structures of the centralizer Zm,n of the wreath product Gn−m in the group algebra of Gn for any n⩾m. We establish the connection between Zm,n and a generalization of degenerate affine Hecke algebras introduced in our earlier work.