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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
Entstehung:
Anmerkungen:
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>