Relative braid group symmetries on quantum groups of Kac–Moody type

• Weinan Zhang ^[1]
  1. [1] University of Virginia

     University of Virginia

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
• Idioma: inglés
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• Resumen

  • Recently, relative braid group symmetries on quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, generalizing that finite-type construction, we establish relative braid group symmetries on quantum groups of locally quasi-split Kac–Moody type. We formulate root vectors for quantum groups in both recursive forms and closed divided power forms. The higher rank formulas of relative braid group symmetries are given by root vectors. We show that the relative braid group symmetries send root vectors to root vectors.