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1998 Fiscal Year Final Research Report Summary

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)
Project Period (FY) 1996 – 1998
Keywordsfinite simple groups / algebraic groups / monster / combinatorics / vertex operator algebras / Hecke algebras
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.

  • Research Products

    (16 results)

All Other

All Publications (16 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 1999-12-08  

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