Abstract Let G be a finite group, let b be a G-invariant block with defect group Q of the normal subgroup H of G, and let b ′ ∈ Z ⁢ ( 𝒪 ⁢ N H ⁢ ( Q ) ) {b^{\prime}\in Z(\mathcal{O}N_{H}(Q))} be the Brauer correspondent of b. We show that the bijection between the blocks of G covering b and the blocks of N G ⁢ ( Q ) {N_{G}(Q)} covering b ′ {b^{\prime}} , induced by a G / H {G/H} -graded basic Morita equivalence between the block extensions b ⁢ 𝒪 ⁢ G {b\mathcal{O}G} and b ′ ⁢ 𝒪 ⁢ N G ⁢ ( Q ) {b^{\prime}\mathcal{O}N_{G}(Q)} , coincides with the Harris–Knörr correspondence.

中文翻译：

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小组评分基本 Morita 等价和 Harris-Knörr 对应

摘要 令 G 为有限群，令 b 为 G 的正常子群 H 的缺陷群 Q 的 G 不变块，令 b ′ ∈ Z ⁢ ( 𝒪 ⁢ NH ⁢ ( Q ) ) {b^{\prime }\in Z(\mathcal{O}N_{H}(Q))} 是 b 的 Brauer 通讯者。我们证明了覆盖 b 的 G 块和覆盖 b ′ {b^{\prime}} 的 NG ⁢ ( Q ) {N_{G}(Q)} 块之间的双射，由 G / H {G /H} - 块扩展 b ⁢ 𝒪 ⁢ G {b\mathcal{O}G} 和 b ′ ⁢ 𝒪 ⁢ NG ⁢ ( Q ) {b^{\prime}\mathcal{O}N_ 之间分级的基本 Morita 等价{G}(Q)} ，与 Harris-Knörr 对应。