An sl_2-type tensor category for the Virasoro algebra at central charge 25 and applications

Robert McRae Yau Mathematical Sciences Center, Tsinghua University Jinwei Yang Shanghai Jiaotong University

Category Theory Mathematical Physics Quantum Algebra Representation Theory mathscidoc:2301.04001

Mathematische Zeitschrift, 303, (2), 32, 2023.2
Let O_25 be the vertex algebraic braided tensor category of finite-length modules for the Virasoro Lie algebra at central charge 25 whose composition factors are the irreducible quotients of reducible Verma modules. We show that O_25 is rigid and that its simple objects generate a semisimple tensor subcategory that is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl_2-modules. We also show that this sl_2-type subcategory is braid-reversed tensor equivalent to a similar category for the Virasoro algebra at central charge 1. As an application, we construct a simple conformal vertex algebra which contains the Virasoro vertex operator algebra of central charge 25 as a PSL_2(C)-orbifold. We also use our results to study Arakawa's chiral universal centralizer algebra of SL_2 at level -1, showing that it has a symmetric tensor category of representations equivalent to Rep PSL_2(C). This algebra is an extension of the tensor product of Virasoro vertex operator algebras of central charges 1 and 25, analogous to the modified regular representations of the Virasoro algebra constructed earlier for generic central charges by I. Frenkel-Styrkas and I. Frenkel-M. Zhu.
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@inproceedings{robert2023an,
  title={An sl_2-type tensor category for the Virasoro algebra at central charge 25 and applications},
  author={Robert McRae, and Jinwei Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20230127164636400727745},
  booktitle={Mathematische Zeitschrift},
  volume={303},
  number={2},
  pages={32},
  year={2023},
}
Robert McRae, and Jinwei Yang. An sl_2-type tensor category for the Virasoro algebra at central charge 25 and applications. 2023. Vol. 303. In Mathematische Zeitschrift. pp.32. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20230127164636400727745.
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