In a recent paper, Dave Benson and Peter Symonds defined a new invariant γ_G(M) for a finite dimensional module M of a finite group G which attempts to quantify how close a module is to being projective. In this paper, we determine this invariant for permutation modules of the symmetric group corresponding to two-part partitions using tools from representation theory and combinatorics.

中文翻译：

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置换模块的Benson-Symonds不变式

在最近的一篇论文，戴夫Benson和彼得·西蒙兹定义的新的不变量γ _ģ（中号为有限维模块）中号有限群G ^其中尝试量化模块的接近程度被投射。在本文中，我们使用表示论和组合论工具确定了与两部分分区相对应的对称组置换模块的不变性。