The Farahat-Higman Algebra of Centralizers of Symmetric Group Algebras

Abstract

We define a generalisation of the Farahat-Higman algebra introduced in [FH59] which replaces the role of the center of the group algebra of the symmetric groups with certain centralizer algebras instead. We prove various structural properties of this new algebra and provide an isomorphism which connects it to the degenerate affine Hecke algebra and the algebra of symmetric functions.