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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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2017: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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 / 導来同値 / 箙 / カルタン不変数 |
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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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Report
(4 results)
Research Products
(36 results)
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[Presentation] Yet small 1-PIMS2016
Author(s)
S. Koshitani
Organizer
Endo-p-permutation and trivial source modules in the representation theory of finite groups
Place of Presentation
スイス連邦工科大学ローザンヌ校 （スイス ローザンヌ市）
Year and Date
2016-09-02
Related Report
Int'l Joint Research / Invited
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