Group theory and related topics

群论及相关主题

• 批准号: 08304003
• 负责人: YAMAKI Hiroyoshi
• 金额: $ 9.92万
• 依托单位: Kumamoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304003/
• 关键词: finite simple groups; algebraic groups; monster; combinatorics; vertex operator algebras; Hecke algebras; アソシェーションスキーム

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.

我们学习了有限、代数、量子群和组合数学，并研究了这些学科的共同性质。H.Yamaki（熊本大学）应用有限单群的分类来了解有限群的性质。室兰工业大学的N.Chigira，山口大学的N.Iiyori和H.Yamaki证明了偶数阶有限群的每个非交换的Sylow子群都包含一个与对合交换的非平凡元素。东京理科大学的T.Shoji研究了约化群的特征标表的计算，并在Lusztig猜想上取得了重大进展。T.Shoji还试图将Coxeter群和Hecke代数的几个性质扩展到复反射群和循环Hecke代数。M.Miyarnoto（筑波大学）从码构造VOA，并对Monster单群的研究做出了贡献。对于VOA，他定义了广义theta函数，并显示其模不变性。T.谷崎（广岛大学）和M.Kashiwara（RIMS）解决了Kazhdan-Lusztig猜想的卡茨穆迪李代数。T.Tanisaki和Y.Morita（广岛大学）构造了抛物准齐次向量空间的量子形变，E.Bannai（九州大学）和M.Ozeki（山形大学）研究了有限环和有限交换群上的几种码，并考虑了它们在模函数上的应用。

项目成果

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)

Masato Sawabe：“Metiuten 单群 M24、M23、M22 共轭类的组合方法”，《日本数学会杂志》51。（1999 年）

千吉良直紀: "Number of Sylow subgroups and p-nilpotence of finite groups" Journal of Algebra. 35. (1998)

Naoki Chiyoshira：“Sylow 子群的数量和有限群的 p 幂零性”《代数杂志》35。（1998）

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)

Naoki Chigira、Nobuo Iiyori 和 Hiroshi Yamaki：“偶数阶有限群的非阿贝尔 Sylow 子群”美国数学会电子研究公告。

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)

Toshiyuki Tanisaki 和 Masaki Kashiwara：“具有负 II 级、非负情况的仿射李代数的 Kazhdan-Lusztig 猜想”杜克数学杂志。

奥間智弘: "The plurigenera of Gorenstein surface singularities" Manuscripta Mathematicae. 94. 187-194 (1997)

Tomohiro Okuma：“Gorenstein 表面奇点的多变性”Manuscripta Mathematicae 94. 187-194 (1997)。