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PreprintarXiv licencearXiv

The double super Yangians in type A for arbitrary 0m 1n-sequences and their bosonic representations

  • Pengfa Xu
  • Hongda Lin
  • Honglian Zhang
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Abstract

In this paper, we introduce the double super Yangian DYh(glm|ns) and DYh(slm|ns) associated with any fixed 0m1n-sequence s. First, we establish an explicit isomorphism between the Drinfeld and R-matrix presentations of DYh(glsm|n). We then generalize the notion of the quantum Berezinian to DYh(glm|ns), and employ it to construct the R-matrix presentation of DYh(slm|ns) and prove that it is isomorphic to the Drinfeld presentation. As an application, we present level-1 bosonic representations for DYh(glm|ns) and DYh(slm|ns) in terms of their Drinfeld current generators.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026double,
  title = {{The double super Yangians in type A for arbitrary $0^m 1^n$-sequences and their bosonic representations}},
  author = {Pengfa Xu and Hongda Lin and Honglian Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.01031},
  eprint = {2608.01031},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.01031},
}
RIS
TY  - UNPB
TI  - The double super Yangians in type A for arbitrary 0^m 1^n-sequences and their bosonic representations
AU  - Pengfa Xu
AU  - Hongda Lin
AU  - Honglian Zhang
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.01031
UR  - https://arxiv.org/abs/2608.01031
AB  - In this paper, we introduce the double super Yangian DY_h(gl_m|n^s) and DY_h(sl_m|n^s) associated with any fixed 0^m1^n-sequence s. First, we establish an explicit isomorphism between the Drinfeld and R-matrix presentations of DY_h(gl^s_m|n). We then generalize the notion of the quantum Berezinian to DY_h(gl_m|n^s), and employ it to construct the R-matrix presentation of DY_h(sl_m|n^s) and prove that it is isomorphic to the Drinfeld presentation. As an application, we present level-1 bosonic representations for DY_h(gl_m|n^s) and DY_h(sl_m|n^s) in terms of their Drinfeld current generators.
ER  -