Analysis of decomposition matrices for sporadic finite simple groups
| Project/Area Number |
22540007
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
HIDA Akihiko 埼玉大学, 教育学部, 准教授 (50272274)
HANAKI Akihide 信州大学, 理学部, 教授 (50262647)
KUNUGI Naoko 東京理科大学, 理学部, 准教授 (50362306)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 有限群論 / モジュラー表現 / 散在型単純群 / モジュラー表現論 / 分解行列 / 群論 |
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| Research Abstract |
It has been clear that the calculations of characters in the sporadic finite simple group J4 which is the main object in this project and its maximal subgroup are not enough for the decision of decomposition matrix of the full defect blocks in J4. We found the concrete way of the construction of modular representations over a field of characteristic 3 by the algebra analysis system GAP using the Amagamation from two representations of maximal subgroups of J4. This construction is deduced from the construction of the ordinary representation of J4. We also proved the irreducible p-module of dimension 1333 of J4 is trivial source module in case that p=3.
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Report
(5 results)
Research Products
(35 results)
