Torsion pairs for quivers and the Weyl groups

• Yuya Mizuno ^[1] ; Hugh Thomas ^[2]
  1. [1] Osaka Prefecture University

     Osaka Prefecture University

     Sakai Ku, Japón

     
  2. [2] University of Quebec at Montreal

     University of Quebec at Montreal

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00563-9
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• Resumen

  • We give an interpretation of the map πc defined by Reading, which is a map from the elements of a Coxeter group to the c-sortable elements, in terms of the representation theory of preprojective algebras. Moreover, we study a close relationship between c-sortable elements and torsion pairs, and give an explicit description of the cofinite torsion classes in the context of the Coxeter group. As a consequence, we give a proof of some conjectures proposed by Oppermann, Reiten, and the second author.