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arXiv · 2609.35067

Isomorphism between the R-matrix and Drinfeld presentations of quantum affine superalgebra for type $\boldsymbol{A}$

Pengfa Xu·Hongda Lin·Honglian Zhang
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Abstract

In this paper, we establish an explicit isomorphism between Drinfeld and R-matrix presentations of the quantum affine superalgebra associated with the general linear Lie superalgebra $\mathfrak{gl}(m|n)$. This result can be viewed as a supersymmetric analogue of the isomorphism between two presentations of the quantum affine algebra $U_{q}(\widehat{\mathfrak{gl}(n)})$ proposed by Frenkel-Ding. Furthermore, employing the quantum Berezinian of $U_{q}(\widehat{\mathfrak{gl}(m|n))}$, we construct the R-matrix presentation of the quantum affine superalgebra $U_{q}(\widehat{\mathfrak{sl}(m|n))}$ and prove the isomorphism between its R-matrix and Drinfeld presentations. Our proof based on the commutative relation between Gaussian generators, $\mathbb{A}$-form and quantum Berezinian.

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Pengfa Xu, Hongda Lin, Honglian Zhang. 2026-09-28. Isomorphism between the R-matrix and Drinfeld presentations of quantum affine superalgebra for type $\boldsymbol{A}$. https://arxiv.org/abs/2609.35067

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