Cyclotomic Nazarov-Wenzl algebras

Abstract

Nazarov \cite{Nazarov:brauer} introduced an infinite dimensional algebra, which he called the \textit{affine Wenzl algebra}, in his study of the Brauer algebras. In this paper we study certain ``cyclotomic quotients'' of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank $r^n(2n-1)!!$ (when $\Omega$ is $\bu$--admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov--Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Weyl algebra (when $\Omega$ is admissible).