2017 Fiscal Year Final Research Report
Broue's conjecture in representation theory of finite groups and related topics
| Project/Area Number |
15K04776
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | ブルエ予想 / アルペリン重み予想 / アルペリン・マッカイ予想 / 表現論 / ブロック / 自明自己準同型加群 |
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| Outline of Final Research Achievements |
In order to solve "Broue's conjecture" we must have the Brauer indecomposability of the Scott modules. We proved it for some cases. As related topics of Broue's conjecture we have two conjectures, say "Alperin's weight conjecture" and "Alperin-McKay conjecture. For the case where the defect group is cyclic we have obtained three results. There is also an important notion "Endo-trivial modules" related to the conjectures. We proved it for dihedral defect groups case which had been an open problem. All the work was joint one with four persons in the UK and Germany. I gave invited talks e.g. in Oberwolfach and Jena in Germany 2015, in EPFL in Lausanne Switzerland 2016, and also in Banff Canada 2017.
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| Free Research Field |
数物系科学
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