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2006 Cyclotomic Nazarov-Wenzl algebras
Susumu Ariki, Andrew Mathas, Hebing Rui
Nagoya Math. J. 182: 47-134 (2006).

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.

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Susumu Ariki. Andrew Mathas. Hebing Rui. "Cyclotomic Nazarov-Wenzl algebras." Nagoya Math. J. 182 47 - 134, 2006.

Information

Published: 2006
First available in Project Euclid: 20 June 2006

zbMATH: 1159.20008
MathSciNet: MR2235339

Subjects:
Primary: 20C08
Secondary: 16G99

Rights: Copyright © 2006 Editorial Board, Nagoya Mathematical Journal

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