中心亏式群上的伽罗瓦等变 Dade-Glauberman-Nagao 对应
A Galois-equivariant Dade-Glauberman-Nagao correspondence with central defect
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中文总结 AI 辅助
本文为中心亏式群上的广义 Dade-Glauberman-Nagao 对应构造了高度为零的普通不可约特征之间的伽罗瓦等变对应，并满足块关系，适用于 Alperin-McKay-Navarro 约化。
中文摘要 AI 辅助
我们为中心亏式群上的广义 Dade-Glauberman-Nagao 对应构造了高度为零的普通不可约特征之间的对应。该对应在群和伽罗瓦自同构下是等变的，并满足 $\mathcal{H}$-三元组之间的块关系。对于每对对应的特征，有一对相关的射影表示实现了匹配的因子集、相等的中心标量、同步的混合比较函数以及每个中间群的相容块对应。该构造使用了中心亏式子群的群代数上的重数代数、剩余半线性实现的归一化积分提升以及分次角同构。它处理了所有中心特征纤维，包括具有非平凡中心特征的纤维。我们还获得了适用于 Alperin-McKay-Navarro 约化中正规 $p$-截面的形式。
英文摘要
We construct a correspondence between ordinary irreducible characters of height zero above the generalized Dade-Glauberman-Nagao correspondence for blocks with central defect. The correspondence is equivariant under group and Galois automorphisms and satisfies a block relation between $\mathcal{H}$-triples. For each pair of corresponding characters, one pair of associated projective representations realizes matching factor sets, equal central scalars, synchronized mixed comparison functions and compatible block correspondences for every intermediate group. The construction uses the multiplicity algebra over the group algebra of the central defect subgroup, a normalized integral lift of a residual semilinear realization, and a graded corner isomorphism. It treats all central-character fibers, including those with nontrivial central character. We also obtain a form suited to normal $p$-sections in an Alperin-McKay-Navarro reduction.
发表机构
- School of Mathematics and Statistics, Central China Normal University（华中师范大学数学与统计学院）
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