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Cyclotomic Nazarov-Wenzl Algebras

Published online by Cambridge University Press:  11 January 2016

Susumu Ariki
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan, ariki@kurims.kyoto-u.ac.jp
Andrew Mathas
Affiliation:
School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia, a.mathas@maths.usyd.edu.au
Hebing Rui
Affiliation:
Department of Mathematics, East China Normal University, 200062 Shanghai, P. R. China, hbrui@math.ecnu.edu.cn
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Abstract

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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 rn(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.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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