In 2020, Brunat–Dudas–Taylor showed that the decomposition matrix of unipotent $\ell $-blocks of a finite reductive group in good characteristic has unitriangular shape, under some conditions on the prime $\ell $, in particular $\ell $ being good. We extend this result to $\ell $ bad by adapting their proof to include the $\ell $-special classes defined by Chaneb.
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Keywords: finite reductive groups, decomposition numbers, character sheaves, generalised Gelfand–Graev representations
Roth, Marie 1
CC-BY 4.0
@article{ART_2025__2_4_537_0,
author = {Roth, Marie},
title = {Unitriangularity of decomposition matrices of the unipotent $\ell $-blocks for simple adjoint exceptional groups},
journal = {Annals of Representation Theory},
pages = {537--574},
publisher = {The Publishers of ART},
volume = {2},
number = {4},
year = {2025},
doi = {10.5802/art.29},
language = {en},
url = {https://art.centre-mersenne.org/articles/10.5802/art.29/}
}
TY - JOUR AU - Roth, Marie TI - Unitriangularity of decomposition matrices of the unipotent $\ell $-blocks for simple adjoint exceptional groups JO - Annals of Representation Theory PY - 2025 SP - 537 EP - 574 VL - 2 IS - 4 PB - The Publishers of ART UR - https://art.centre-mersenne.org/articles/10.5802/art.29/ DO - 10.5802/art.29 LA - en ID - ART_2025__2_4_537_0 ER -
%0 Journal Article %A Roth, Marie %T Unitriangularity of decomposition matrices of the unipotent $\ell $-blocks for simple adjoint exceptional groups %J Annals of Representation Theory %D 2025 %P 537-574 %V 2 %N 4 %I The Publishers of ART %U https://art.centre-mersenne.org/articles/10.5802/art.29/ %R 10.5802/art.29 %G en %F ART_2025__2_4_537_0
Roth, Marie. Unitriangularity of decomposition matrices of the unipotent $\ell $-blocks for simple adjoint exceptional groups. Annals of Representation Theory, Volume 2 (2025) no. 4, pp. 537-574. doi : 10.5802/art.29. https://art.centre-mersenne.org/articles/10.5802/art.29/
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