H-三元组的块关系与Clifford理论
Block Relations and Clifford Theory for H-Triples
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中文总结 AI 辅助
本文研究有限群H-三元组的块关系，证明满足混合比较函数恒等式和块条件的Clifford对应定理，并建立归纳与粘合准则，为Galois等变局部-整体对应提供工具。
中文摘要 AI 辅助
我们研究有限群的H-三元组之间的块关系。我们证明了Clifford对应定理，其中一对相关联的射影表示在每个中间群上同时满足混合比较函数恒等式和块条件。由此产生的对应保持相对特征标高度，并为每对对应块提供一个共同的缺陷群。我们还建立了归纳和粘合结果，包括一个允许不等Clifford指数的归纳准则。直积、圈积和环境群的改变在同一框架内处理。这些结果为Galois等变局部-整体对应提供了特征标三元组工具。
英文摘要
We study block relations between H-triples of finite groups. We prove a Clifford correspondence theorem in which a single pair of associated projective representations satisfies both the mixed comparison-function identities and the block conditions on every intermediate group. The resulting correspondence preserves relative character heights and yields a common defect group for each pair of corresponding blocks. We also establish induction and gluing results, including an induction criterion that allows unequal Clifford indices. Direct products, wreath products and changes of ambient group are treated within the same framework. These results provide character-triple tools for Galois-equivariant local-global correspondences.
发表机构
- Central China Normal University（华中师范大学）
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