Analysis of decomposition matrices for sporadic finite simple groups

显然，作为本课题主要研究对象的偶发有限单群J 4及其极大子群的特征标的计算，对于判定J 4中满亏块的分解矩阵是不够的。利用代数分析系统GAP对J_4的极大子群的两个表示进行了映射，找到了构造特征为3的域上模表示的具体方法.这个结构是从J 4的普通表示的结构推导出来的。证明了当p=3时，J 4的1333维不可约p-模是平凡源模。

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.