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This article is cited in 10 scientific papers (total in 10 papers)
A $q$-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
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
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.
Linking options:
https://www.mathnet.ru/eng/sigma120 https://www.mathnet.ru/eng/sigma/v2/p92
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Abstract page: | 296 | Full-text PDF : | 73 | References: | 43 |
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