Abstract. Nazarov [Naz96] 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 r n (2n − 1)!! (when Ω is u-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 Wenzl algebra.
This paper classifies the simple modules of the cyclotomic Hecke algebras of type G(r, 1, n) and the affine Hecke algebras of type A in arbitrary characteristic. We do this by first showing that the simple modules of the cyclotomic Hecke algebras are indexed by the set of "Kleshchev multipartitions".
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.