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無限次元の群における非コンパクト部分群のコンパクト性

无限维群中非紧子群的紧性

基本信息

批准号：
14654014
负责人：
小林俊行
金额：
$ 0.9万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Exploratory Research
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

项目摘要

『無限次元の群における非コンパクト部分群がコンパクト的に振舞う現象』を指導原理として、等質多様体の不連続群の理論とユニタリ表現の分岐則を結びつける例を具体的に計算し、その視点をより明確にするべく以下の研究を行った。1.離散群の作用がいつ固有不連続となるかを判定する有効な方法をみつけることは、非リーマン等質空間における不連続群論で重要な問題である。変換群が簡約リー群の場合は、この問題に対する大きな進展が最近なされたが、一方、Auslander予想に現れるようなアファイン変換群に対しては原理的な理解がなされていない。そこで、より一般的な原理を探るための実験として、R^nにおけるZ^<n-1>の固有不連続な冪零作用を初等的な計算で分類し、その変形空間を具体的に決定した。3次元のローレンツ空間形に関するGoldman予想とは異なり、変形空間において固有不連続性が不安定になる特異点が存在するという発見は特に注目すべき点と考える(論文準備中)。また、この手法を推し進めて、吉野太郎氏は冪零等質空間への群作用に関するLipsman予想を4次元の場合に肯定的に解決した。2.非リーマン等質空間の不連続群に関する未解決問題の提起、格子の存在問題の現状、種々の手法などについての総説を著し(論文[1])、日本数学会で概説講演を行った。3.擬リーマン空間形において(局所的)共形変換群のユニタリ表現を等長部分群に制限したときのスペクトラムを計算した。この結果は、非コンパクトな部分群への制限に連続スペクトラムが現れないというコンパクト的な現象を、擬リーマン多様体上で幾何的に実現したものであり、解析的にはあるウルトラ双曲型の偏微分方程式と楕円型作用素の同時スペクトル展開を具体的に決定することに対応する(論文[2,3,4,5])。

The vibration and dance images of some groups of people with limited dimensions are not related to those of some groups. They guide the principles of the theory of multi-body data, such as the theory of multi-body data, the theory of multi-body data, and the results of the examples of specific calculations and data points that clearly indicate the following research lines. 1. There are some methods for determining whether there is a method for determining whether there is an inherent non-link between air and space users, such as non-contact, and so on. On the basis of the group agreement, we have made a great progress in the recent development of the group, one party, and the Auslander would like to understand the principle of the group. The general principles of calculation and classification are discussed in this paper. The basic principles of calculation and classification are discussed in this paper. The basic principles of calculation and general principles are discussed in this paper, the principles of calculation and general principles are discussed in this paper, the principles of calculation and general principles are discussed in this paper, the principles of calculation and general principles are discussed in detail. The 3-dimensional space Goldman is intended to show that there is an inherent disconnection, instability, instability and special points of interest (in preparation for the article). The effects of air-to-air communication, such as the introduction of advanced technology and Yoshino Taro's zero, are very important in the analysis of the Lipsman of the four-dimensional system. two。 Non-linear space users, such as unsolved problems, grid problems, various techniques, and the Japanese Mathematical Association will conduct an overview of the exhibition. 3. There is a limit on the calculation of the equivalent length of the conformal group (of the bureau). The result of the experiment, the partial group of the non-linear system, and the partial partial differential equation of the partial differential equation of the hyperbolic equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic equation of the hyperbolic differential equation, the analytical partial differential equation of the hyperbolic equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic differential equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation of the hyperbolic equation, the partial differential equation 4]).