UNITRIANGULARITY OF DECOMPOSITION MATRICES OF THE UNIPOTENT ℓ-BLOCKS FOR SIMPLE ADJOINT EXCEPTIONAL GROUPS

Marie Roth (1, 2, 3, 4)

1 AMU - Aix Marseille Université
2 I2M - Institut de Mathématiques de Marseille
3 CNRS - Centre National de la Recherche Scientifique
4 RPTU Kaiserslautern-Landau

In 2020, BrunatDudasTaylor showed that the decomposition matrix of unipotent ℓ-blocks of a nite reductive group in good characteristic has unitriangular shape, under some conditions on the prime ℓ, in particular ℓ being good. We extend this result to ℓ bad by adapting their proof to include the ℓ-special classes dened by Chaneb.

Mots clés: Finite reductive groups; Decomposition numbers; Character sheaves; generalised Gelfand-Graev representations

Domaines: Théorie des représentations [math.RT]

Marie Roth. UNITRIANGULARITY OF DECOMPOSITION MATRICES OF THE UNIPOTENT ℓ-BLOCKS FOR SIMPLE ADJOINT EXCEPTIONAL GROUPS. 2024. ⟨hal-04474518⟩