1998 Fiscal Year Final Research Report Summary
Group theory and related topics
| Project/Area Number |
08304003
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
YAMAKI Hiroyoshi Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (60028199)
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| 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)
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| Project Period (FY) |
1996 – 1998
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| Keywords | finite simple groups / algebraic groups / monster / combinatorics / vertex operator algebras / Hecke algebras |
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| 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.
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Research Products
(16 results)
