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THE INDUCTIVE BLOCKWISE ALPERIN WEIGHT CONDITION FOR TYPE AND THE PRIME
Journal of the Australian Mathematical Society ( IF 0.5 ) Pub Date : 2020-11-06 , DOI: 10.1017/s1446788720000439
ZHICHENG FENG , GUNTER MALLE

We establish the inductive blockwise Alperin weight condition for simple groups of Lie type $\mathsf C$ and the bad prime $2$ . As a main step, we derive a labelling set for the irreducible $2$ -Brauer characters of the finite symplectic groups $\operatorname {Sp}_{2n}(q)$ (with odd q), together with the action of automorphisms. As a further important ingredient, we prove a Jordan decomposition for weights.



中文翻译:

类型和 PRIME 的感应 BLOCKWISE ALPERIN 重量条件

我们为李类型$\mathsf C$ 和坏素数 $2$ 的简单群建立了归纳块 Alperin 权重条件 。作为主要步骤,我们为 有限辛群 $\operatorname {Sp}_{2n}(q)$ (带有奇数q )的不可约 $2$ -Brauer 字符以及自同构作用推导出了一个标记集。作为更重要的成分,我们证明了权重的 Jordan 分解。

更新日期:2020-11-06
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