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

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.

Authors

Publication Details

Journal
Symmetry Integrability and Geometry Methods and Applications
Published
2024-11-22
DOI
https://doi.org/10.3842/sigma.2024.105
Primary Topic
Algebraic structures and combinatorial models
Type
article
Field-Weighted Citation Impact
0.00

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article

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

Xianghua Wu, Hongda Lin, Honglian Zhang
Symmetry Integrability and Geometry Methods and Applications
Algebraic structures and combinatorial models
article

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

Xianghua Wu, Hongda Lin, Honglian Zhang
article en

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.

Symmetry Integrability and Geometry Methods and Applications
Natural Science Foundation of Shanghai, National Natural Science Foundation of China
Openalex Percentile: Top 68%
Algebraic structures and combinatorial models
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