论文标题
在特征3中保持不可还原的对称组和交替组的不可还原旋转表示
Irreducible spin representations of symmetric and alternating groups which remain irreducible in characteristic 3
论文作者
论文摘要
对于任何有限的组$ g $和任何Prime $ p $，一个人都可以询问哪些普通不可约的表示形式在特征$ p $或更一般的特征上仍然是不可约的，在特征$ p $中，哪些表示均具有同质性。在本文中，当$ g $是对称或交替组的适当双重盖时，我们以$ p = 3 $解决了这个问题。我们获得了一个分类，除非某种与旋转岩石块有关的分区家族。我们的技术涉及诱导和限制，学位计算，分解投影特征以及Kleshchev和Livesey在自旋岩石块上的最新结果。
For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$, or more generally, which representations remain homogeneous in characteristic $p$. In this paper we address this question for $p=3$ when $G$ is a proper double cover of the symmetric or alternating group. We obtain a classification except in the case of a certain family of partitions relating to spin RoCK blocks. Our techniques involve induction and restriction, degree calculations, decomposing projective characters and recent results of Kleshchev and Livesey on spin RoCK blocks.
