Unitriangularity of decomposition matrices of the unipotent ${\ell}$-blocks for simple adjoint exceptional groups

Abstract: In 2020, Brunat-Dudas-Taylor showed that the decomposition matrix of unipotent ${\ell}$-blocks of a nite 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 dened by Chaneb.