Group theory and related topics

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。熊本大学的H.Yamaki(熊本大学)应用有限单群的分类来了解有限群的性质。其中，N.Chigira(Muroran理工学院)，N.Iiyori(山口大学)和H.Yamaki证明了偶数阶有限群的每个非交换Sylow子群都包含一个与对合可交换的非平凡元。T.Shoji(东京科学大学)研究了约化群的特征标表的计算，并在Lusztig猜想的基础上取得了重大进展。T.Shoji还试图将Coxeter群和Hecke代数的一些性质推广到复反射群和循环Hecke代数。M.Miya noto(筑波大学)从码构造了VOA，并对Monster单群的研究做出了贡献。T.Tanisaki(广岛大学)和M.Kashiwara(RIMS)解决了Kac-Moody李代数的Kazhdan-Lusztig猜想。T.Tanisaki和Y.Morita(广岛大学)构造了抛物型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，并考虑了它在模函数中的应用。

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.