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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 331, Pages 170–198 (Mi znsl254)  

This article is cited in 13 scientific papers (total in 13 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
References:
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
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 141, Issue 4, Pages 1479–1493
DOI: https://doi.org/10.1007/s10958-007-0053-1
Bibliographic databases:
UDC: 512.552.8
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Nik06}
\by P.~P.~Nikitin
\paper The centralizer algebra of the diagonal action of the group $GL_n(\mathbb C)$ in a~mixed tensor space
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XIV
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 331
\pages 170--198
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2251346}
\zmath{https://zbmath.org/?q=an:1135.20032}
\elib{https://elibrary.ru/item.asp?id=9172490}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 141
\issue 4
\pages 1479--1493
\crossref{https://doi.org/10.1007/s10958-007-0053-1}
\elib{https://elibrary.ru/item.asp?id=13544723}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846847965}
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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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