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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
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.
Received: November 18, 2019; in final form May 10, 2020; Published online May 21, 2020
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.
Linking options:
https://www.mathnet.ru/eng/sigma1580 https://www.mathnet.ru/eng/sigma/v16/p43
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