• Medientyp: E-Artikel
  • Titel: Unitriangular shape of decomposition matrices of unipotent blocks
  • Beteiligte: Brunat, Olivier; Dudas, Olivier; Taylor, Jay
  • Erschienen: Annals of Mathematics, 2020
  • Erschienen in: Annals of Mathematics
  • Sprache: Englisch
  • DOI: 10.4007/annals.2020.192.2.7
  • ISSN: 0003-486X; 1939-8980
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  • Beschreibung: <p>We show that the decomposition matrix of unipotent 𝓁-blocks of a finite reductive group 𝐆(𝔽<italic> <sub>q</sub> </italic>) has a unitriangular shape, assuming <italic>q</italic> is a power of a good prime and 𝓁 is very good for 𝐆. This was conjectured by Geck in 1990 as part of his PhD thesis. We establish this result by constructing projective modules using a modification of generalised Gelfand-Graev characters introduced by Kawanaka. We prove that each such character has at most one unipotent constituent which occurs with multiplicity one. This establishes a 30 year old conjecture of Kawanaka.</p>