Solution of Broue's conjecture in representation Theory of finite groups

对于“Broue猜想”，我们已经证明了以下内容。首先，我们证明了Broue猜想的一个零星的单群，说Janko的单群J_4，与N.Kunugi和K. Waki的联合工作。其次，我们证明了Broue猜想也是一个零星的单群，说Harada-Norton单群HN，联合工作与J. Mueller。我们还证明了一种工具，通过它我们可以找到平凡的源模块，与N. Kunugi联合工作。与M.霍洛威和N.Kunugi一起，我们还证明了一个关于Rouquier猜想的定理。该猜想是Broue猜想的一种类似物。最后，我们与Y. Yoshii共同证明了有限群块的Cartan矩阵的特征值的一个结果。

For the subject "Broue's conjecture" we have proven the following. First of all, we proved Broue's conjecture for one of the sporadic simple groups, say the Janko's simple group J4, joint work with N.Kunugi and K.Waki. Secondly, we proved the Broue's conjecture also for one of the sporadic simple groups, say Harada-Norton simple group HN, joint work with J.Mueller. We also proved a kind of tool by which we can find out trivial source modules, joint work with N.Kunugi. With M.Holloway and N.Kunugi, we proved also a theorem which was on Rouquier's conjecture. The conjecture is a kind of analogue of Broue's conjecture. Finally we proved a result on eigenvalues of the Cartan matrices of blocks of finite groups, jointly with Y.Yoshii.