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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 331, Pages 170–198
(Mi znsl254)
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This article is cited in 14 scientific papers (total in 14 papers)
The centralizer algebra of the diagonal action of the group $GL_n(\mathbb C)$ in a mixed tensor space
P. P. Nikitin St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
We consider the walled Brauer algebra $Br_{k,l}(n)$ introduced by V. Turaev and K. Koike.
We prove that this algebra is a subalgebra of the Brauer algebra and that it is isomorphic, for sufficiently large $n\in\mathbb N$, to the centralizer algebra of the diagonal
action of the group $GL_n(\mathbb C)$ in a mixed tensor space. We also give a presentation of the algebra $Br_{k,l}(n)$ by generators and relations. For the generic parameter, the
algebra is semisimple, and in this case we describe the Bratteli diagram for the family
of algebras under consideration and give realizations of the irreducible representations. We also give a new, more natural, proof of the formulas for the characters of the walled Brauer
algebras.
Received: 16.06.2006
Citation:
P. P. Nikitin, “The centralizer algebra of the diagonal action of the group $GL_n(\mathbb C)$ in a mixed tensor space”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Zap. Nauchn. Sem. POMI, 331, POMI, St. Petersburg, 2006, 170–198; J. Math. Sci. (N. Y.), 141:4 (2007), 1479–1493
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https://www.mathnet.ru/eng/znsl254 https://www.mathnet.ru/eng/znsl/v331/p170
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Abstract page: | 310 | Full-text PDF : | 103 | References: | 51 |
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