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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 043, 49 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.043 (Mi sigma1580) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$

Naihuan Jinga, Ming Liubc, 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
Full-text PDF (583 kB) Citations (13)
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DOI: https://doi.org/10.3842/SIGMA.2020.043
Abstract: Following the approach of Ding and Frenkel [Comm. Math. Phys. 156 (1993), 277–300] for type $A$, we showed in our previous work [J. Math. Phys. 61 (2020), 031701, 41 pages] that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the quantum affine algebra yields the Drinfeld generators in all classical types. Complete details for type $C$ were given therein, while the present paper deals with types $B$ and $D$. The arguments for all classical types are quite similar so we mostly concentrate on necessary additional details specific to the underlying orthogonal Lie algebras.
Keywords: $R$-matrix presentation, Drinfeld new presentation, universal $R$-matrix, Gauss decomposition.
Funding agency Grant number
National Natural Science Foundation of China 11531004
11701182
Simons Foundation 523868
Natural Science Foundation of Guangdong Province 2019A1515012039
Australian Research Council DP180101825
Jing acknowledges the National Natural Science Foundation of China grant 11531004 and Simons Foundation grant 523868. Liu acknowledges the National Natural Science Foundation of China grant 11531004, 11701182 and the Guangdong Natural Science Foundation grant 2019A1515012039. Liu and Molev acknowledge the support of the Australian Research Council, grant DP180101825.
Received: November 18, 2019; in final form May 10, 2020; Published online May 21, 2020
Bibliographic databases:
Document Type: Article
MSC: 17B37, 17B69
Language: English
Citation: Naihuan Jing, Ming Liu, Alexander Molev, “Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$”, SIGMA, 16 (2020), 043, 49 pp.
Citation in format AMSBIB
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\by Naihuan~Jing, Ming~Liu, Alexander~Molev
\paper Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$
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\vol 16
\papernumber 043
\totalpages 49
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    • This publication is cited in the following 13 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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