论文标题
在对称组的重量块二次重量块上
On Ext-Quivers of Blocks of Weight Two for Symmetric Groups
论文作者
论文摘要
在本文中，我们研究了重量2的对称组块，这是奇数特征$ p $的字段。我们开发了一种算法，该算法将两个这样的块的震动与示波器介绍的两个这样的块形成$（2：1）$。然后，我们将算法应用于$ p $ cores是挂钩分区的块，以明确确定这些块的震颤。结果，我们得出的结论是，两个$ p $ blocks $ b_1 $和$ b_2 $的对称重量$ 2 $的$ p $ - cores是挂钩分区的，并且仅当$ b_2 $或其conjugate块与$ b_1 $相同的scopes类时，且仅当$ b_2 $或其conjugate块。
In this paper we investigate blocks of symmetric groups of weight 2 over fields of odd characteristic $p$. We develop an algorithm that relates the quivers of two such blocks forming a $(2:1)$ pair, as introduced by Scopes. We then apply the algorithm to blocks whose $p$-cores are hook partitions, in order to explicitly determine the quivers of these blocks. As a consequence we conclude that two $p$-blocks $B_1$ and $B_2$ of symmetric groups of weight $2$ whose $p$-cores are hook partitions are Morita equivalent if and only if $B_2$ or its conjugate block is in the same Scopes class as $B_1$.
