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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 145, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.145 (Mi sigma1681) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2020.145
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.
Funding agency Grant number
Australian Research Council DP180101825
We acknowledge the support of the Australian Research Council, grant DP180101825.
Received: August 19, 2020; in final form December 25, 2020; Published online December 28, 2020
Bibliographic databases:
Document Type: Article
MSC: 17B37
Language: English
Citation: Naihuan Jing, Ming Liu, Alexander Molev, “Representations of Quantum Affine Algebras in their $R$-Matrix Realization”, SIGMA, 16 (2020), 145, 25 pp.
Citation in format AMSBIB
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