有限群表示中重要的猜想，如Alperin猜想、Broué猜想、Dade猜想，目前都约化到了单群或者拟单群。具体群的表示，尤其是单群及拟单群的表示，是当前有限群表示研究的主要任务。具体群的表示有其自身的意义。在具体群表示的研究中，也会出现一些具有理论意义的现象。据此，本项目提出研究Broué猜想与Donovan猜想对一些具体的群的主块或unipotent块是否成立。预期将证明一些有限群的主块与其Brauer对应之间存在保持群自同构的splendid Rickard等价，如Sylow 3-子群是9阶初等交换群或Sylow 2-子群是交换群的有限群、交错群、零散单群等；给出酉群的重为2的unipotent块与一些射影特殊线性群的主块的代数结构的刻画，证明Broué猜想对酉群的重为2的unipotent块与一些射影特殊线性群的主块成立；证明Donovan猜想对一些射影特殊线性群的主块成立。

Main conjectures in representation theory of finite groups, such as Alperin Conjecture, Broué Conjecture and Dade Conjecture, were reduced to simple groups or to quasisimple groups. Representation of special groups, such as simple groups and quasisimple groups, is the main task of current representation theory of finite groups. Hereby we propose the verification of Broué Conjecture and Donovan Conjecture for the principal blocks or unipotent blocks of some special groups. We expect to prove the existence of equivariant splendid equivalence between the principal blocks of some finite groups and their Brauer correspondents, such as finite groups with Sylow 3-group of order 9 or abelian Sylow 2-subgroup, Alternating groups，Sporadic groups and so on, to characterize unipotent blocks of unitary groups with weight 2 and the principal blocks of some projective special linear groups and prove Broué Conjecture and Donovan Conjecture for these blocks, and to prove Donovan Conjecture for the principal blocks of some projective special linear groups.