Tilting complex and Perverse equivalence in Representation theory

在主持人的帮助下，我们研究了一种对应于两项倾斜的反常等价。一般来说，并不是所有的两个任期的倾斜都是反常的对等。具有全部二项倾斜复形的代数的条件可以用Jasso约化来描述。此外，还对预射影代数的特殊情况进行了研究。其中我们确定了两项倾斜的倒等价类型，并将其与对称群的组合学联系起来。我们还建立了Rouquier-Okuyama倾斜复形与倒等价之间的联系，正如项目开始时所建议的那样。除了以上的主要进展外，我们与名古屋大学的Aaron Chan共同完成了一些对称群表示的p-复形的同调工作。与TUS的工作进行得令人满意。

With the help of the host we have investigate a type of perverse equivalence that correspond to two-term tilting. In general not all two-term tilting is a perverse equivalence. The condition of an algebra with all two-term tilting complex can be described using Jasso reduction. There is also an investigation into the particular case of preprojective algebra. In which we have determined the type of two-term tilting that is a perverse equivalence and related it to combinatorics of symmetric group.Also we have established a link between Rouquier-Okuyama tilting complex to perverse equivalence, as suggested at the start of the project. There are still a lot of questions remain unanswered but we managed to get the results we hoped for.Beside the above main progresses we have managed to conclude the work in homology of p-complexes of some symmetric group representations, a joint work with Aaron Chan in Nagoya University. The work with TUS is satisfactorily conducted.