TY - JOUR
T1 - Unitriangular shape of decomposition matrices of unipotent blocks
AU - Taylor, Jonathan
AU - Dudas, Olivier
AU - Brunat, Olivier
PY - 2020/9/9
Y1 - 2020/9/9
N2 - 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].
AB - 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].
UR - http://dx.doi.org/10.4007/annals.2020.192.2.7
U2 - 10.4007/annals.2020.192.2.7
DO - 10.4007/annals.2020.192.2.7
M3 - Article
SN - 0003-486X
VL - 192
SP - 583
EP - 663
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 2
ER -