RUS  ENG
Full version
JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2024 Volume 20, 105, 38 pp. (Mi sigma2107)

$R$-Matrix Presentation of Quantum Affine Superalgebra for Type $\mathfrak{osp}(2m+1|2n)$

Xianghua Wuab, Hongda Linca, Honglian Zhangda

a Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
b School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541000, P.R. China
c Shenzhen International Center for Mathematics, SUSTech, Guangdong 518055, P.R. China
d Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, P.R. China

Abstract: In our preceding research, we introduced the Drinfeld presentation of the quantum affine superalgebra associated to the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m>0$. We provided the isomorphism between its Drinfeld–Jimbo presentation and Drinfeld presentation using braid group actions as a fundamental method. Based on this work, our current study delves into its $R$-matrix presentation, wherein we establish a clear isomorphism between the $R$-matrix presentation and the Drinfeld presentation. In particular, our contribution extends the investigations of Jing, Liu and Molev concerning quantum affine algebra in type BCD to the realm of supersymmetry.

Keywords: quantum affine superalgebra, $R$-matrix presentation, Drinfeld presentation, universal $R$-matrix.

MSC: 17B37, 17B69

Received: June 19, 2024; in final form November 15, 2024; Published online November 22, 2024

Language: English

DOI: 10.3842/SIGMA.2024.105


ArXiv: 2406.09800


© Steklov Math. Inst. of RAS, 2025