Unitriangular shape of decomposition matrices of unipotent blocks

Jonathan Taylor, Olivier Dudas, Olivier Brunat

Research output: Contribution to journalArticlepeer-review


We show that the decomposition matrix of unipotent ℓ-blocks of a finite reductive group G(Fq) has a unitriangular shape, assuming q is a power of a good prime and ℓ is very good for G. This was conjectured by Geck [23] in 1990. 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, see [42, 2.4.5].
Original languageEnglish
Pages (from-to)583-663
JournalAnnals of Mathematics
Issue number2
Publication statusPublished - 9 Sept 2020


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