Study of Mathematical Sciences by Algebraic Methods

用代数方法研究数学科学

基本信息

批准号：
03302001
负责人：
HOTTA Ryoshi
金额：
$ 3.84万
依托单位：
TOHOKU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03302001/
关键词：
Invariant Theory Duality Quantum Groups Algebraic Groups Moduli of Vector Bundles Hypergeometric Differential Equations Conformal Fields Number Theory 表現論ゼータ関数場の理論指標層 b関数 9アナログ capelli恒等式 D加群ベクトル束

项目摘要

The following conferences are organized and/or supported according to the main point of this project: 1.Symposium of Algebraic Geometry(1991.10.1-4,Kyoto Univ.) 2.New Trend of Invariant Theory(1991.12.16-18,Osaka Univ.) 3.Duality as Phenomenon(1992.8.4-6,Hakodate) 4.Quantum Groups and Related Topics(1992.10.3-5,Nagoya Univ.) 5.Representations of Algebraic Groups(1992.10.29-31,Tohoku Univ.)The details are in the separated booklet "Report of the Results of the Project" and here is only a summary.In Conf.1, the structure of moduli of vector bundles, which is also interested in mathematical physics, was a main topic and many related results were reported.Conf.2 was organized by the head investigator and some of the others. There we tried to investigate the role of invariant theory, one of the main themes of classical algebra, in the modern analysis including mathematical physics. Varieties of topics were hypergeometric differential equations, representations of quantum groups, and conformal field theory.Conf.3 is rather an unusual meeting where distinguished mathematicians of quite varieties of fields attended and discussed the concept "Duality" in mathematics (and even outer world). Many problems and results were proposed from number theory to physics. The proceedings will be soon published by the organizers.For Conf.4, we supported the publication of its proceedings.Conf.5 is for discussions of recent results and problems in somewhat traditional representation theory. Together with three foreign experts as participants,many results were reported including their technical points.

根据该项目的要点组织和/或支持以下会议：1。代数几何体的符合（1991.10.1-4，Kyoto Univ。）2。不变理论的新趋势（1991.12.16-16-16-18，Osaka Univ，Osaka Univ。主题（1992.10.3-5，nagoya univ。）5。代数组的代表（1992.10.29-31，tohoku univ。）详细信息在“项目结果的报告”中分开，这里只是一个摘要。报道。Conf.2由首席调查员和其他一些人组织。在那里，我们试图研究不变理论的作用，这是古典代数的主要主题之一，在包括数学物理学在内的现代分析中。主题的品种是超几何差分方程，量子群的表示和保形场理论。Conf.3是一次不寻常的会议，在这里，有很多田野的数学家参加并讨论了数学中的概念“二元性”（甚至外部世界）。从数字理论到物理学提出了许多问题和结果。诉讼程序将很快由组织者发表。对于conf.4，我们支持其诉讼的发布。conf.5用于讨论一些传统代表理论中的最新结果和问题。与三名外国专家一起作为参与者，报告了许多结果，包括他们的技术观点。