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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 092, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.092
(Mi sigma120)
 

This article is cited in 10 scientific papers (total in 10 papers)

$q$-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra

Mark J. Hopkins, Alexander I. Molev

School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
References:
Abstract: We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra $\mathrm U_q(\widehat{\mathfrak{gl}}_n)$. We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand–Tsetlin character or ($q$-character). We also apply the quantum Sylvester theorem to construct a $q$-analogue of the Olshanski algebra as a projective limit of certain centralizers in $\mathrm U_q(\mathfrak{gl}_n)$ and show that this limit algebra contains the $q$-Yangian as a subalgebra.
Keywords: quantum affine algebra; quantum Sylvester theorem; skew representations.
Received: October 14, 2006; Published online December 26, 2006
Bibliographic databases:
Document Type: Article
MSC: 81R10
Language: English
Citation: Mark J. Hopkins, Alexander I. Molev, “A $q$-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra”, SIGMA, 2 (2006), 092, 29 pp.
Citation in format AMSBIB
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\by Mark J.~Hopkins, Alexander I.~Molev
\paper A~$q$-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
\jour SIGMA
\yr 2006
\vol 2
\papernumber 092
\totalpages 29
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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