Quivers with relations for symmetrizable Cartan matrices IV: crystal graphs and semicanonical functions

• Christof Geiss ^[1] ; Bernard Leclerc ^[2] ; Jan Schröer ^[3]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
  2. [2] Centre National de la Recherche Scientifique

     Centre National de la Recherche Scientifique

     París, Francia

     
  3. [3] Universität Bonn, Germany

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 3283-3348
• Idioma: inglés
• DOI: 10.1007/s00029-018-0412-4
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• Resumen

  • We generalize Lusztig’s nilpotent varieties, and Kashiwara and Saito’s geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of generalized preprojective algebras. Conjecturally these functions yield semicanonical bases of the enveloping algebras of the positive part of symmetrizable Kac–Moody algebras.