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.a yamaki应用有限单群的分类来了解有限群的性质。其中，Muroran工业大学的N.Chigira，山口大学的N.Iiyori和h.a yamaki证明了偶阶有限群的每个非阿贝尔Sylow子群都包含一个非平凡元，该非平凡元与对合交换。东京科学大学的t.o shoji研究了约化群的特征表的计算，并在Lusztig猜想上取得了重大进展。T.Shoji也尝试将Coxeter群和Hecke代数的若干性质推广到复反射群和循环Hecke代数。m . miyarnoto （University of Tsukuba）从码构造了VOA，并对Monster简单群的研究做出了贡献。对于VOA，他定义了广义的θ函数，并证明了它们的模不变性。广岛大学的t.t anisaki和kariwara解决了Kac-Moody李代数的Kazhdan-Lusztig猜想。日本广岛大学的T.Tanisaki和Y.Morita构造了抛物型预齐次向量空间的量子变形，日本九州大学的e . bannai和山形大学的M.Ozeki研究了有限环和有限阿贝尔群上的几种码，并思考了它们在模函数中的应用。

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.