论文标题
Spepht模块一级同谋的组合方法
A combinatorial approach to first degree cohomology of Specht modules
论文作者
论文摘要
使用纯粹的组合方法，我们计算了由两个部分分区索引的SpepHT模块的第一度共同体，而特征$ p \ ge 3 $。这些组合方法还使我们能够通过微不足道的模块获得SpecHT模块的所有非切片扩展的明确描述。将这项工作应用于具有两个以上部分的分区，我们能够为Donkin和Geranios的作品提供了完全组合的界限。我们还获得了韦伯（Weber）的结果，这是韦伯（Weber）给出了遥远的条件，确定了分区，而该分区的第一个共同体学是微不足道的。
Using purely combinatorial methods we calculate the first degree cohomology of Specht modules indexed by two part partitions over fields of characteristic $p\ge 3$. These combinatorial methods also allow us to obtain an explicit description of all of the non-split extensions of the Specht module, $S^λ$, by the trivial module. Applying this work to partitions with more than two parts we are able to give an entirely combinatorial proof of the bound on the dimension of the first degree cohomology given by work of Donkin and Geranios. We also obtain as a corollary a result of Weber giving a far reaching condition determining partitions for which the first cohomology of the Specht module is trivial.
