Studies on spaces with algebraic group action and representation theory

代数群作用空间与表示论的研究

• 批准号: 13640039
• 负责人: SEKIGUCHI Jiro
• 金额: $ 1.92万
• 依托单位: Tokyo University of Agriculture and Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640039/
• 关键词: Nilpotent orbit; Exceptional Lie algebra; Hyperbolic orbit; Compactification; Regular polyhedra; Monodromy; 単純リー環; 対称対; 鏡映群; Simple Lie algebra; nilpotent orbit; symmetric pair; hyperbolic orbit; compactification

1. J. Sekiguchi studied an imbedding of nilpotent orbits of an exceptional real simple Lie algebra into another. (A joint work with Professor D. Z. Djokovic)2. J. Sekiguchi studied hyperbolic orbits of real semisimple Lie algebras and compactificiations of them. This work was reported at NUS-JSPS Workshop on ALGEBRA held in Singapore 2001 and also done at a meeting held in RIMS, Kyoto Univ., 2002.3. J. Sekiguchi studied the relationship between regular polyhedral groups and monodromy groups of Appell's hypergeometric functions. (A joint work with Prof. M. Kato (Univ. of Ryukyus))

1. J. Sekiguchi研究了一个特殊的真实的简单李代数的幂零轨道到另一个的嵌入。（与D教授合作。Z.德约科维奇）2. J. Sekiguchi研究了真实的半单李代数的双曲轨道及其紧化。这项工作在2001年新加坡举行的NUS-JSPS代数研讨会上作了报告，并在京都大学RIMS举行的一次会议上作了报告，2002.3. J. Sekiguchi研究了阿佩尔超几何函数的正则多面体群与单值群之间的关系。（与M教授合作。加藤（琉球大学）

项目成果

D.Z.Djokovic, J.Sekiguchi: "Mapping of nilpotent orbits under embedding of real forms of exceptional complex Lie algebras"Asian J.Math.. 6. 409-431 (2002)

D.Z.Djokovic、J.Sekiguchi：“异常复李代数实数形式嵌入下的幂零轨道映射”Asian J.Math.. 6. 409-431 (2002)

E. Bannai, M., Koike, A. Munemasa and J. Sekiguchi: "Some results on modular groups-Subgroups of the modular group whose ring of modular forms is a polynomial ring"Advanced Studies in Pure Math.. 32. 245-254 (2001)

E. Bannai，M.，Koike，A. Munemasa 和 J. Sekiguchi：“模群的一些结果 - 模群的子群，其模形式的环是多项式环”纯数学高级研究.. 32. 245-

D. Z. Djokovic and J. Sekiguchi: "Mapping of nilpotent orbits under embeddings of real forms of exceptional complex Lie algebras"Asian J. Math.. 6. 409-432 (2002)

D. Z. Djokovic 和 J. Sekiguchi：“异常复李代数实数形式嵌入下的幂零轨道映射”Asian J. Math.. 6. 409-432 (2002)

D. Z. Djokovic and J. Sekiguchi: "Nilpotent orbits of the complex pairs whose restricted root systems are of type F_4"Theory ofl Lie Groups and Manifolds, by R. Miyaoka and H. Tamaru, Sophia Kokyuroku in Math.. No.45. 39-56 (2003)

D. Z. Djokovic 和 J. Sekiguchi：“受限根系为 F_4 型的复数对的幂零轨道”李群和流形理论，作者：R. Miyaoka 和 H. Tamaru，Sophia Kokyuroku，《数学》第 45 期。

D.Z.Djokovic, N.Lemire, J.Sekiguchi: "The closure ordering of adjoint nilpotent ornits in so(p, q)"Tohoku Math.J.. 53. 395-442 (2001)

D.Z.Djokovic、N.Lemire、J.Sekiguchi：“so(p, q) 中伴随幂零鸟的闭包排序”Tohoku Math.J.. 53. 395-442 (2001)