Coxeter orbits and Brauer trees
Coxeter orbits and Brauer trees
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DOI：
10.1016/j.aim.2012.02.011
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发表时间：
2010-11
影响因子：
1.7
通讯作者：
O. Dudas
中科院分区：
文献类型：
--
作者：
O. Dudas
研究了与Coxeter元相关的Deligne-Lusztig簇的模系数上同调。在上同调的无挠假设下，当q模π的阶为Coxeter数时，得到了有限约化群G（Fq）的主π-块的几个结果.这些结果包括块的平面嵌入Brauer树的确定（如Hiss，Lübeck和Malle（1995）在[25]中所述）和Broué猜想的几何版本（Broué和Malle，1993，[7]）所预测的导出等价性。
We study the cohomology with modular coefficients of Deligne–Lusztig varieties associated to Coxeter elements. Under some torsion-free assumption on the cohomology we derive several results on the principal ℓ-block of a finite reductive group G(Fq) when the order of q modulo ℓ is assumed to be the Coxeter number. These results include the determination of the planar embedded Brauer tree of the block (as conjectured by Hiss, Lübeck and Malle (1995) in [25]) and the derived equivalence predicted by the geometric version of Brouéʼs conjecture (Broué and Malle, 1993, [7]).