Unitriangular shape of decomposition matrices of unipotent blocks

• 成果类型: Article
• 署名作者: Brunat, Olivier; Dudas, Olivier; Taylor, Jay
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.192.2.7
• 发表日期: 2020
• 页码: 583-663
• 关键词: gelfand-graev representations; nilpotent orbits; finite-groups; basic sets; character sheaves; brauer characters; reductive groups; lie type; support; numbers

摘要

We show that the decomposition matrix of unipotent l-blocks of a finite reductive group G(F-q) 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 in 1990 as part of his PhD thesis. 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.