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Group theory and related topics

Research Project

Project/Area Number 08304003
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

YAMAKI Hiroyoshi  Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (60028199)

Co-Investigator(Kenkyū-buntansha) 坂内 英一  九州大学, 数理学研究科, 教授 (10011652)
谷崎 俊之  広島大学, 理学部, 教授 (70142916)
SHOJI Toshiaki  Science University of Tokyo, Faculty of Science and Engineering, Professor, 理工学部, 教授 (40120191)
MIYAMOTO Masahiko  University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (30125356)
YOSHIDA Tomoyuki  Hokkaido University, Graduate School of Science, Professor, 理学研究科, 教授 (30002265)
日比 孝之  大阪大学, 理学研究科, 教授 (80181113)
兼田 正治  大阪市立大学, 理学部, 教授 (60204575)
川中 宣明  大阪大学, 理学研究科, 教授 (10028219)
竹内 光弘  筑波大学, 数学系, 教授 (00015950)
木村 弘信  熊本大学, 理学部, 教授 (40161575)
Project Period (FY) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥15,500,000 (Direct Cost: ¥15,500,000)
Fiscal Year 1998: ¥4,300,000 (Direct Cost: ¥4,300,000)
Fiscal Year 1997: ¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 1996: ¥4,600,000 (Direct Cost: ¥4,600,000)
Keywordsfinite simple groups / algebraic groups / monster / combinatorics / vertex operator algebras / Hecke algebras / アソシェーションスキーム
Research Abstract

We studied finite, algebraic, quantum groups and combinatorial mathematics, and looked at common properties of these subjects.
H.Yamaki (Kumamoto University) applied the classification of finite simple groups to know properties of finite groups. Among other things N.Chigira (Muroran Institute of Technology), N.Iiyori (Yamaguchi University) and H.Yamaki proved that every non-abelian Sylow subgroups of finite groups of even order contains a non-trivial element, which commutes with an involution.
T.Shoji (Science University of Tokyo) studied to calculate the character tables of reductive groups and made a significant progress on the Lusztig's conjecture. T.Shoji also tried to extend several properties of Coxeter groups and Hecke algebras to complex reflection groups and cyclic Hecke algebras.
M.Miyarnoto (University of Tsukuba) constructed VOA from codes and contributed to the study of Monster simple group. For VOA he defined generalized theta functions and showed their modular invariance.
T.Tanisaki (Hiroshima University) and M.Kashiwara (RIMS) solved the Kazhdan-Lusztig conjecture for Kac-Moody Lie algebra. T.Tanisaki and Y.Morita (Hiroshima University) constructed the quantum deformations of parabolic prehomogeneous vector spaces.
E.Bannai (Kyushu University) and M.Ozeki (Yamagata University) studied several codes over finite rings and finite abelian groups and thought about the applications to modular functions.

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] 八牧,宏美: "Non-abelian Sylow subgroups of finite groups of even order" Electronic Research Announcements of AMS. 88-90 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 庄司,俊明: "Shintani descent for special linear groups" Journal of Algebra. 199. 175-228 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 宮本,雅彦: "Representation theory of code vertex operator algebra" Journal of Algebra. 201. 115-150 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 谷崎,俊之: "Kazhdan-Lusztig conjecture for affine Lie algebras with negative level II non-negative case" Duke Mathematical Journal. 84・3. 771-813 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 千吉良,直紀: "Number of Sylow subgroups and p-nilpotonce of finite groups" Journal of Algebra. 201. 71-85 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 吉田,知行: "Classical problems in group theory" Sugaku Expositions, AMS. 9. 169-184 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 木村,達雄: "概均質ベクトル空間" 岩波書店, 368 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 坂内,英一: "球面上の代数的組合せ論" シュプリンガー東京, (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Naoki Chigira, Nobuo Iiyori, and Hiroshi Yamaki: "Non-abelian Sylow subgroups of finite groups of even order" Electronic Research Announcements of the American Mathematical Society. 4. 88-90 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Toshiaki Shoji: "Shintani descent for special linear groups" Journal of Algebra. 199. 175-228 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masahiko Miyamoto: "Representation theory of code vertex operator algebra" Journal of Algebra. 201. 115-150 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Toshiyuki Tanisaki, and Masaki Kashiwara: "Kazhdan-Lusztig conjecture for affine Lie algebras with negative level II,non-negative case" Duke Mathematical Journal. 84. 771-813 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Naoki Chigira: "Number of Sylow subgroups and p-nilpotence of finite groups" Journal of Algebra. 201. 71-85 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tomoyuki Yoshida: "Classical problems in group theory" Sugaku Expositions, American Mathematical Society. 9. 169-184 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tatsuo Kimura: Prehomogeneous vector spaces (in Japanese). Iwanami, 368 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Eiichi Bannai, and Etsuko Bannai: Algebraic combinatorics on spheres (in Japanese). Springer-Tokyo, (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 八牧宏美: "Non-abelian Sylow subgroups of finitc groups of iven order" Electronic Research Announcements of AMS. 4. 80-90 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 千吉良直紀: "Number of Sylori subgroups and p-nibpotence of finite groups" Journal of Algebra. 201. 71-85 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 千吉良直紀: "Finite groups nhose abelian subgroups have consecutive orders" Osaka Jounal of Mathmatics. 35. 439-445 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 飯寄信保: "Prine graphs and brauer characters" Journal of Group Thcory. 1. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 澤辺正人: "2-radical subgroups of the Conway simple group CO1." Jounal of Algebra. 210. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 澤辺正人: "A combinatorial approach to the conjugacy classes of the Metiuten simple groups M24,M23,M22." Journal of the mathematical Society of Japan. 51. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 木村達雄: "概均質ベクトル空間" 岩波書店, 368 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宮西正宣: "複素数への招待" 日本評論社, 196 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 八牧宏美: "Finite groups with metacyclic automorphism groups" Northeastern Mathematical Journal. 18・1. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 千吉良直紀: "Generating alternating groups" Hokkaido Mathematical Journal. 26・2. 435-438 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 千吉良直紀: "Number of Sylow subgroups and p-nilpotence of finite groups" Journal of Algebra. 35. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 千吉良直紀: "Finite groups whose abelian subgroups have consecutivq orders" Osaka Journal of Mathematics. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 兼田正治: "Some generalities on D-modules in positive characteristic" Pacific Journal of Mathematics.

    • Related Report
      1997 Annual Research Report
  • [Publications] 奥間智弘: "The plurigenera of Gorenstein surface singularities" Manuscripta Mathematicae. 94. 187-194 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 八牧宏美: "A conjecture of Trobenius" Sugaku Expositions. 9・1. 69-85 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 木村弘信: "A normal form of Hamiltonian systems of several time variables with a regular singularity" clourral of Differential Equations. 127・2. 337-364 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 坂内英一: "Construction of Jacobi forms from certain combinatorial polynomials" Proceedings of Japan Academy. 72・1. 12-15 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 平峰豊: "On tactical decompositions of class number 2" Geometriae Dedicata. 62. 35-52 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 千吉良直紀: "The-solutions of X^d=1 in finite groups" Journal of Algebra. 180・. 653-661 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 千吉良直紀: "Generating alternating groups" Hokkaido Mathematical Journal. 26・1. (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 千吉良直紀: "Generating alternating groups" Hokkaido Mathematical Journal. 26・1. (1997)1-4

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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