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Representations of Quantum Affine Algebras in their $R$-Matrix Realization
Naihuan Jinga, Ming Liub, Alexander Molevc a Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
b School of Mathematics, South China University of Technology, Guangzhou, 510640, China
c School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
Abstract:
We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B$, $C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix realization.
We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the $R$-matrix and Drinfeld presentations of the Yangians.
Keywords:
$R$-matrix presentation, Drinfeld polynomials, highest weight representation, Gauss decomposition.
Received: August 19, 2020; in final form December 25, 2020; Published online December 28, 2020
Citation:
Naihuan Jing, Ming Liu, Alexander Molev, “Representations of Quantum Affine Algebras in their $R$-Matrix Realization”, SIGMA, 16 (2020), 145, 25 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1681 https://www.mathnet.ru/eng/sigma/v16/p145
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Abstract page: | 65 | Full-text PDF : | 23 | References: | 13 |
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