Cyclotomic Nazarov-Wenzl algebras

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Nazarov Nazarov:brauer introduced an infinite dimensional algebra, which he called the 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 rⁿ(2n-1)!! (when Ω is --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 Ω is admissible).