本项目将从以下三个方面展开研究：研究亏群交换的2-块，从单群上亏群交换的2-块的结构定理出发，试图验证这种情形下块形式的Alperin权猜想的约化条件；研究弱的Broue交换亏群猜想和特征标层面的Rouquier猜想约化的相关问题；研究9阶初等交换亏群的块，试图证明该块与其Brauer对应是perfect isometric。

The proposal will be carried out from the following aspects.Firstly, we investigate 2-blocks with abelian defect groups, use the structure theorem of 2-blocks with abelian defect groups in simple groups and try to verify the inductive conditions for the blockwise version of the Alperin weight conjecture. Secondly, we investigate the reductions of both Rouquier's conjecture and Broue's conjecture to simple groups at the level of characters. Lastly, we investigate 3-blocks with elementary abelian defect group of order 9 and try to prove that blocks and their Brauer correspondences are perfect isometric in this case.