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Knizhnik-Zamolodchikov equations in Deligne categories

Representation Theory 2025-04-07 v2 Mathematical Physics math.MP Quantum Algebra

Abstract

We consider the Knizhnik-Zamolodchikov equations in Deligne Categories in the context of (glm,gln)(\mathfrak{gl}_m,\mathfrak{gl}_{n}) and (som,so2n)(\mathfrak{so}_m,\mathfrak{so}_{2n}) dualities. We derive integral formulas for the solutions in the first case and compute monodromy in both cases.

Keywords

Cite

@article{arxiv.2504.02266,
  title  = {Knizhnik-Zamolodchikov equations in Deligne categories},
  author = {Pavel Etingof and Ivan Motorin and Alexander Varchenko and Isaac Zhu},
  journal= {arXiv preprint arXiv:2504.02266},
  year   = {2025}
}