Solution of Broue's conjecture in representation theory of finite groups
Project/Area Number |
23540007
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Chiba University |
Principal Investigator |
KOSHITANI Shigeo 千葉大学, 理学(系)研究科(研究院), 教授 (30125926)
|
Co-Investigator(Renkei-kenkyūsha) |
KUNUGI Naoko 東京理科大学, 理学部第一部, 准教授 (50362306)
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Project Period (FY) |
2011-04-28 – 2015-03-31
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Project Status |
Completed (Fiscal Year 2014)
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Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | ブルエ予想 / 表現論 / 有限群 / ブロック / 森田同値 / 導来同値 / アルペリン予想 / マッカイ予想 / 不足群 |
Outline of Final Research Achievements |
For the subject "Broue's conjecture", we have been able to prove the following. First of all, we proved Broue's conjecture for the sproradic simple Conway group Co3 completely. Then, we prove Broue's conjecture of character version for an arbitrary block with elementary abelian defect group of order 8. This was the first improvement after Brauer did 35 years ago. Further, we proved Broue's conjecture for the sporadic Janko simple group J4 more precisely. We proved Broue's conjecture also for the double cover 2HS of the sporadic Higman-Sims simple group HS. Finally we proved Broue's conjecture for the sporadic Conway simple group Co1, and as a byproduct we could determine the 3-decomposition numbers for Co1 in part.
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Report
(5 results)
Research Products
(26 results)
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[Presentation] Small 1-PIMs2014
Author(s)
S. Koshitani
Organizer
ロンドン・代数セミナー
Place of Presentation
ロンドン・インペリアル・カレッジ
Year and Date
2014-11-27
Related Report
Invited
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