Ordinary modules for affine vertex operator superalgebras

Abstract

Let g be a basic classical Lie superalgebra and let ĝ be the corresponding affine Lie superalgebra. In this paper, we first prove that a Cartan subalgebra acts semisimply on ordinary modules for the simple affine vertex operator superalgebra L_ĝ(k,0) at boundary admissible level k. Then we prove that the category 𝒪_k^ord(g) of ordinary L_ĝ(k,0)-modules is finite, semisimple and 𝒪_k^ord(g) is exactly the category KL_k(g) of finite-length generalized modules for the affine vertex operator superalgebra L_ĝ(k,0).Thus 𝒪_k^ord(g) is a braided tensor supercategory. Furthermore, we obtain the rigidity of the supercategory 𝒪_k^ord(g) and thus it is a ribbon supercategory. Finally, we conclude that 𝒪_k^ord(g) is a ribbon fusion supercategory.

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BibTeX RIS

BibTeX

@misc{li2026ordinary,
  title = {{Ordinary modules for affine vertex operator superalgebras}},
  author = {Huaimin Li and Qing Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01774},
  eprint = {2610.01774},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01774},
}

RIS

TY  - UNPB
TI  - Ordinary modules for affine vertex operator superalgebras
AU  - Huaimin Li
AU  - Qing Wang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01774
UR  - https://arxiv.org/abs/2610.01774
AB  - Let g be a basic classical Lie superalgebra and let ĝ be the corresponding affine Lie superalgebra. In this paper, we first prove that a Cartan subalgebra acts semisimply on ordinary modules for the simple affine vertex operator superalgebra L_ĝ(k,0) at boundary admissible level k. Then we prove that the category 𝒪_k^ord(g) of ordinary L_ĝ(k,0)-modules is finite, semisimple and 𝒪_k^ord(g) is exactly the category KL_k(g) of finite-length generalized modules for the affine vertex operator superalgebra L_ĝ(k,0).Thus 𝒪_k^ord(g) is a braided tensor supercategory. Furthermore, we obtain the rigidity of the supercategory 𝒪_k^ord(g) and thus it is a ribbon supercategory. Finally, we conclude that 𝒪_k^ord(g) is a ribbon fusion supercategory.
ER  -

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