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

Symmetry Integrability and Geometry-Methods and Applications

article

Naihuan Jing¹  Ming Liu²  Alexander Molev³ 

[1] Department of Mathematics, North Carolina State University;School of Mathematics, South China University of Technology;School of Mathematics and Statistics, University of Sydney

关键词: R-matrix presentation;    Drinfeld new presentation;    universal R-matrix;    Gauss decomposition;   

DOI  :  10.3842/SIGMA.2020.043

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown