2019 Fiscal Year Annual Research Report
Tilting complex and Perverse equivalence in Representation theory
| Project/Area Number |
17F17814
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| Research Institution | Nagoya University |
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Principal Investigator |
伊山 修 名古屋大学, 多元数理科学研究科, 教授 (70347532)
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| Co-Investigator(Kenkyū-buntansha) |
WONG HON YIN 名古屋大学, 多元数理科学研究科, 外国人特別研究員
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| Project Period (FY) |
2017-11-10 – 2020-03-31
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| Keywords | Homological algebra / triangulated category / Perverse Equivalence / Torsion class / Mutation / Preprojective algebra / Symmetric Group Representations / Okuyama tilting complex |
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| Outline of Annual Research Achievements |
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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| Research Progress Status |
令和元年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和元年度が最終年度であるため、記入しない。
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