Cyclotomic Nazarov-Wenzl algebras
Susumu Ariki, Andrew Mathas, and Hebing Rui
Source: Nagoya Math. J. Volume 182 (2006), 47-134.
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 $\Omega$ is $\mathbf{u}$-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.
Primary Subjects: 20C08
Secondary Subjects: 16G99
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.nmj/1150810004
Mathematical Reviews number (MathSciNet):
MR2235339
Zentralblatt MATH identifier:
1159.20008
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