Naihuan Jing, Ming Liu, Alexander Molev, “Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$”, SIGMA, 2020, том 16,043, 49 стр.

Эта публикация цитируется в 17 статьях

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

Naihuan Jing^a, Ming Liu^bc, Alexander Molev^c

^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

Аннотация: 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.

Ключевые слова: $R$-matrix presentation, Drinfeld new presentation, universal $R$-matrix, Gauss decomposition.

MSC: 17B37, 17B69

Поступила: 18 ноября 2019 г.; в окончательном варианте 10 мая 2020 г.; опубликована 21 мая 2020 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2020.043