Analysis of decomposition matrices for sporadic finite simple groups

结果表明，仅计算作为本课题主要研究对象的零星有限简单群J4及其最大子群中的字符，不足以确定J4中全缺陷块的分解矩阵。在代数分析系统GAP中，利用J4的极大子群的两个表示的重叠，找到了构造特征为3的域上的模表示的具体方法。这个结构是从J4的普通表示的结构中推导出来的。我们还证明了J4的1333维不可约p模在p=3时是平凡源模。

It has been clear that the calculations of characters in the sporadic finite simple group J4 which is the main object in this project and its maximal subgroup are not enough for the decision of decomposition matrix of the full defect blocks in J4. We found the concrete way of the construction of modular representations over a field of characteristic 3 by the algebra analysis system GAP using the Amagamation from two representations of maximal subgroups of J4. This construction is deduced from the construction of the ordinary representation of J4. We also proved the irreducible p-module of dimension 1333 of J4 is trivial source module in case that p=3.