| 研究実績の概要 |
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.
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