2009 Fiscal Year Final Research Report
Modular representation analysis of sporadic finite simple groups by computers
| Project/Area Number |
19540004
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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 |
WAKI Katsushi Yamagata University, 理学部, 教授 (30250591)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAMOTO Izumi 山梨大学, 医学工学総合研究部, 教授 (60126654)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 有限群 / 分解行列 / モジュラー表現論 / 散在型単純群 |
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| Research Abstract |
Irreducible Brauer characters of maximal subgroups of the sporadic simple group J_4 are calculated by Fong-Reynolds's theorem on characteristic of all odd primes. With this results, we can determine the almost irreducible characters of the sporadic simple group J_4 which is not belonged in the principal blocks. These irreducible Brauer characters of J_4 are used to prove that the Brou¶e conjecture for J_4 is in the affirmative. Moreover the calculation of projective characters in the principal block is also stared.
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