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

TL;DR

This paper establishes an isomorphism between the $R$-matrix presentation and the Drinfeld presentation of the quantum affine superalgebra associated with $rak{osp}(2m+1|2n)$, extending prior work to supersymmetric cases.

Contribution

It introduces the $R$-matrix presentation for this superalgebra and proves its isomorphism with the Drinfeld presentation, expanding the understanding of quantum affine superalgebras in supersymmetry.

Findings

Established the $R$-matrix presentation for $rak{osp}(2m+1|2n)$ superalgebra.

Proved the isomorphism between $R$-matrix and Drinfeld presentations.

Extended quantum affine algebra results from type BCD to supersymmetric cases.

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.