Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 105, 38 pages      arXiv:2406.09800      https://doi.org/10.3842/SIGMA.2024.105

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

Xianghua Wu ab, Hongda Lin ac and Honglian Zhang ad
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

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

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.

Key words: quantum affine superalgebra; $R$-matrix presentation; Drinfeld presentation; universal $R$-matrix.

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