Poisson brackets and coaction maps of regularized holonomies of the KZ equation

• Anton Alekseev ^[1] ; Florian Naef ^[2] ; Muze Ren ^[1]
  1. [1] Université de Genève

     Université de Genève

     Genève, Suiza

     
  2. [2] Trinity College Dublin

     Trinity College Dublin

     Irlanda

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-025-01123-9
• Enlaces
  • Texto completo
• Resumen

  • We derive explicit closed formulas for the Kirillov-Kostant-Souriau (KKS) coaction maps of open path regularized holonomies of the Knizhnik-Zamolodchikov (KZ) equation, and the corresponding Poisson brackets for the Lie algebra gl(N, C). Our main technical tool is a certain projection of the generalized pentagon equation of Alekseev et al. Generalized Pentagon equation, arXiv:2402.19138 [math.QA] (2025).

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