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Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras

Robert McRae Tsinghua University

Mathematical Physics Quantum Algebra Representation Theory mathscidoc:2204.22002

Advances in Mathematics, 374, 107351, 2020.11
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra g^, from g-module homomorphisms. When g=sl_2, these results extend previous joint work with J. Yang, but the method used here is different. Here, we construct intertwining operators by solving Knizhnik-Zamolodchikov equations for three-point correlation functions associated to g^, and we identify obstructions to the construction arising from the possible non-existence of series solutions having a prescribed form.
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@inproceedings{robert2020vertex,
  title={Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras},
  author={Robert McRae},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415171757647373052},
  booktitle={Advances in Mathematics},
  volume={374},
  pages={107351},
  year={2020},
}
Robert McRae. Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras. 2020. Vol. 374. In Advances in Mathematics. pp.107351. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415171757647373052.
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