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Cyclotomic Nazarov-Wenzl Algebras

Published online by Cambridge University Press:  11 January 2016

Susumu Ariki ,
Andrew Mathas  and
Hebing Rui
Susumu Ariki
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan, [email protected]
Andrew Mathas
Affiliation:
School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia, [email protected]
Hebing Rui
Affiliation:
Department of Mathematics, East China Normal University, 200062 Shanghai, P. R. China, [email protected]
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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

20C0816G99
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 182: Special Issue Celebrating the 60th Birthday of George Lusztig , June 2006 , pp. 47 - 134
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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