论文标题
$ \ ell $ - 本地紧凑型组的权重
Weights for $\ell$-local compact groups
论文作者
论文摘要
在本说明中，我们启动了$ \ Mathcal {f} $ - $ \ ell $ - local $ -local compact组$ \ mathcal {f} $的权重，对带有离散的torus $ t $的离散$ \ ell $ -toral $ -toral $ s $ s $。由阿尔珀林（Alperin）的体重猜想的动机，对简单的谎言类型组的构想，我们猜想是，当$ t $是$ s $ $ s $ of $ \ mathcal {f} $的独特最大亚伯族子群时 - cogacy- cogacy- cogacy- $ s $的每个元素，$ s $的每个元素$ \ nathcal {f} $ - 其Weyl群的普通不可还原特征。通过将$ \ MATHCAL {F} $的结构理论与循环缺陷组的块理论相结合，我们可以在$ \ Mathcal {f} $很简单且$ | s：t |的情况下给出此猜想的证明。 = \ ell $。我们还提出并提供证据证明在这种情况下，鲁滨逊的普通重量猜想的高度零案例的类似物。
In this note, we initiate the study of $\mathcal{F}$-weights for an $\ell$-local compact group $\mathcal{F}$ over a discrete $\ell$-toral group $S$ with discrete torus $T$. Motivated by Alperin's Weight Conjecture for simple groups of Lie-type, we conjecture that when $T$ is the unique maximal abelian subgroup of $S$ up to $\mathcal{F}$-conjugacy and every element of $S$ is $\mathcal{F}$-fused into $T$, the number of weights of $\mathcal{F}$ is bounded above by the number of ordinary irreducible characters of its Weyl group. By combining the structure theory of $\mathcal{F}$ with the theory of blocks with cyclic defect group, we are able to give a proof of this conjecture in the case when $\mathcal{F}$ is simple and $|S:T| =\ell$. We also propose and give evidence for an analogue of the height zero case of Robinson's Ordinary Weight conjecture in this setting.
