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Isomorphism between the R-matrix and Drinfeld presentations of quantum affine superalgebra for type 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 gl(m|n). This result can be viewed as a supersymmetric analogue of the isomorphism between two presentations of the quantum affine algebra Uq(gl(n)̂) proposed by Frenkel-Ding. Furthermore, employing the quantum Berezinian of Uq(gl(m|n))̂, we construct the R-matrix presentation of the quantum affine superalgebra Uq(sl(m|n))̂ and prove the isomorphism between its R-matrix and Drinfeld presentations. Our proof based on the commutative relation between Gaussian generators, 𝔸-form and quantum Berezinian.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026isomorphism,
  title = {{Isomorphism between the R-matrix and Drinfeld presentations of quantum affine superalgebra for type $\boldsymbolA$}},
  author = {Pengfa Xu and Hongda Lin and Honglian Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35067},
  eprint = {2609.35067},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35067},
}
RIS
TY  - UNPB
TI  - Isomorphism between the R-matrix and Drinfeld presentations of quantum affine superalgebra for type A
AU  - Pengfa Xu
AU  - Hongda Lin
AU  - Honglian Zhang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35067
UR  - https://arxiv.org/abs/2609.35067
AB  - 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 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(gl(n)̂) proposed by Frenkel-Ding. Furthermore, employing the quantum Berezinian of U_q(gl(m|n))̂, we construct the R-matrix presentation of the quantum affine superalgebra U_q(sl(m|n))̂ and prove the isomorphism between its R-matrix and Drinfeld presentations. Our proof based on the commutative relation between Gaussian generators, 𝔸-form and quantum Berezinian.
ER  -