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2009 Fiscal Year Final Research Report

Modular representation analysis of sporadic finite simple groups by computers

Research Project

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Project/Area Number 19540004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionYamagata University

Principal Investigator

WAKI Katsushi  Yamagata University, 理学部, 教授 (30250591)

Co-Investigator(Kenkyū-buntansha) MIYAMOTO Izumi  山梨大学, 医学工学総合研究部, 教授 (60126654)
Project Period (FY) 2007 – 2009
Keywords有限群 / 分解行列 / モジュラー表現論 / 散在型単純群
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.

  • Research Products

    (10 results)

All 2009 2008 2007

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (4 results)

  • [Journal Article] On the decomposition numbers of J_42009

    • Author(s)
      K. Waki
    • Journal Title

      Journal of Algebra 321

      Pages: 2171-2186

    • Peer Reviewed
  • [Journal Article] New extremal formally self-dual even codes of length 302009

    • Author(s)
      M. Harada, K. Waki
    • Journal Title

      Advances in Mathematics of Communications 3

      Pages: 311-316

    • Peer Reviewed
  • [Journal Article] A Construction of Designs from PSL(2, q) and PGL(2, q), q=1 mod 6, on q+2 Points2009

    • Author(s)
      I. Miyamoto
    • Journal Title

      Proceedings of Algorithmic Algebraic Combinatorics and Groebner Bases

      Pages: 279-284

    • Peer Reviewed
  • [Journal Article] A Combinatorial Approach to Doubly Transitive Permutation Groups2008

    • Author(s)
      I. Miyamoto
    • Journal Title

      Discrete Mathematics 308

      Pages: 3073-3081

    • Peer Reviewed
  • [Journal Article] Broue abelian defect group conjecture holds for the Janko simple group J_42008

    • Author(s)
      S. Koshitani, N. Kunugi, K. Waki
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1438-1456

    • Peer Reviewed
  • [Journal Article] A Computation of Some Multiply Homogeneous Super-schemes from Transitive Permutation Groups2007

    • Author(s)
      I. Miyamoto
    • Journal Title

      Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computations

      Pages: 293-298

    • Peer Reviewed
  • [Presentation] On the decomposition numbers of J_42009

    • Author(s)
      脇克志
    • Organizer
      研究集会 代数的組合せ論および関連する群と代数
    • Place of Presentation
      信州大学
    • Year and Date
      2009-11-18
  • [Presentation] About Decomposition Numbers of J_42008

    • Author(s)
      脇克志
    • Organizer
      第41回環論および表現論シンポジウム
    • Place of Presentation
      静岡大学
    • Year and Date
      2008-09-07
  • [Presentation] GAPによる既約 Brauer 指標の計算2007

    • Author(s)
      脇克志
    • Organizer
      代数学と計算2007
    • Place of Presentation
      首都大学
    • Year and Date
      2007-12-04
  • [Presentation] J_4の分解行列について2007

    • Author(s)
      脇克志
    • Organizer
      有限群草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2007-08-04

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Published: 2011-06-18   Modified: 2016-04-21  

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