Decomposition matrices for exceptional groups at d=4

2014/10/14 by Olivier Dudas, Dudas, Olivier, Gunter Malle +1
Mathematics · #20C20 #20C33 #20G05 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C20 #msc:20C33 #msc:20G05

paper · pdf · doi:10.48550/arxiv.1410.3754

arxiv created 2014/11/04 · arxiv updated 2014/11/05

Abstract

We determine the decomposition matrices of unipotent ℓ-blocks of defect Φ₄² for exceptional groups of Lie type up to a few unknowns. For this we employ the new cohomological methods of the first author, together with properties of generalized Gelfand-Graev characters which were recently shown to hold whenever the underlying characteristic is good.

Related

• Decomposition matrices for groups of Lie type in non-defining characteristic
• Unitriangularity of decomposition matrices of the unipotent ℓ-blocks for simple adjoint exceptional groups
• Jordan correspondence and block distribution of characters
• Decomposition numbers for the principal Φ_2n-block of Sp_4n(q) and SO_4n+1(q)
• Symmetric group blocks of small defect