Abstract In this paper characters of the normalizer of d-split Levi subgroups in SL n ( q ) and SU n ( q ) are parametrized with a particular focus on the Clifford theory between the Levi subgroup and its normalizer. These results are applied to verify the Alperin-McKay conjecture for primes l with l ∤ 6 ( q 2 − 1 ) and the Alperin weight conjecture for l-blocks of those quasi-simple groups with abelian defect. The inductive Alperin-McKay condition and inductive Alperin weight condition by the second author are verified for certain blocks of SL n ( q ) and SU n ( q ) .

中文翻译：

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关于 A 型简单群的 Alperin-McKay 猜想

摘要 本文参数化了SL n ( q ) 和SU n ( q ) 中d-split Levi 子群的归一化器的性质，特别关注Levi 子群与其归一化器之间的Clifford 理论。这些结果被用于验证具有 l ∤ 6 ( q 2 − 1 ) 的素数 l 的 Alperin-McKay 猜想和具有阿贝尔缺陷的拟单群的 l-block 的 Alperin 权重猜想。对于SL n (q) 和SU n (q) 的某些块，验证了第二作者的归纳Alperin-McKay 条件和归纳Alperin 权重条件。