2018 Fiscal Year Annual Research Report
Tilting complex and Perverse equivalence in Representation theory
| Project/Area Number |
17F17814
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
伊山 修 名古屋大学, 多元数理科学研究科, 教授 (70347532)
|
|---|
| 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
|
|---|
| Project Period (FY) |
2017-11-10 – 2020-03-31
|
| Keywords | homological algebra / DG module / silting theory / triangulated category / Serre subcategory / torsion class / perverse equivalence / mutation |
|---|
| Outline of Annual Research Achievements |
There are now a deeper understanding to differential graded module category (dg category) and silting theory. In particular the notion of perverse equivalence can be generalised to such categories. These will be similar to an application of mutation continuously. That means we can probably determine case-by-case if any equivalence given is perverse. However, it will be difficult to construct any interesting perverse equivalence, or discussing any useful combinatorics, without any extra information of the category.
In parallel to the main research theme, I am studying the p-homology of some complex of permutation modules, in collaboration with Aaron Chan in Nagoya University. We can completely determine the homology of the said complex and also hope to enrich the theory of symmetric group representations.
Up till very recently I have received news there is a group in Tokyo University of Science (TUS) is studying perverse equivalence. There seems to be some collaboration possible.
|
| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We have some new conclusions from this project. Besides that there is some collaboration that can be expected to further this topic.
|
| Strategy for Future Research Activity |
I am hoping to start collaboration with TUS, which I hope will be able to enrich the theory and examples of perverse equivalence.
|
