权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Theory of branching laws of unitary representations and non-commutative harmonic analysis by transformation groups of geometric structures

酉表示分支律理论和几何结构变换群的非交换调和分析

基本信息

批准号：
14340043
负责人：
KOBAYASHI Toshiyuki
金额：
$ 5.82万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

The branching law is the irreducible decomposition of a group representation when restricted to a subgroup (e.g. decomposition of tensor products, breaking symmetry in physics,...). Analysis of branching laws is one of principal subjects in representation theory. Nevertheless, very little has been studied on branching laws of unitary representations of reductive groups, except for some special cases until mid 1990s, partly because of analytic difficulties arising from infinite dimensions.Our main results during this period are :1.To publish the basic theory of branching laws of unitary representations with emphasis on discrete decomposable cases and its applications to representation theory itself, non-commutative harmonic analysis, and topology of locally symmetric spaces.2.To construct the canonical representations of the conformal groups of pseudo-Riemannian manifolds by means of the Yamabe operator. In particular, we use this machinery for the study of minimal representations of in … More definite orthogonal groups. Besides, we find (conformal) conservation laws of solutions to certain ultra-hyperbolic equations. Branching laws when restricted to isometry groups play an important role in our analysis (joint with B.Orsted).3.To make a unified approach to multiplicity-free theorems of the biholomorphic transformation groups of complex manifolds by means of orbit-preserving anthi-holomorphic maps. In particular, we use this machinery for the study of multiplicity-free tensor product representations of general linear groups.4.In the late 1980, I initiated the study of discontinuous groups for pseudo-Riemannian homogeneous spaces. In the memorial volume of A.Borel, I published a survey article on this area, and also gave new criteria for the existence of co-compact discontinuous groups for semisimple symmetric spaces and their tangential symmetric spaces (joint with T.Yoshino). Besides, the deformation spaces of discontinuous groups are investigated.5.On these topics, I gave one-hour invited lectures in various international conferences, including ICM 2002, Pan-African Congress 2004 (plenary address), and Asian Congress 2005. Less

分支律是群表示在受限于子群时的不可约分解（例如张量积的分解，物理学中的对称破缺，.）。分支律的分析是表示论的主要研究课题之一。然而，直到20世纪90年代中期，除了一些特殊情况外，关于约化群酉表示的分支律的研究很少，部分原因是无穷维引起的分析困难。我们在这一时期的主要结果是：1.发表酉表示的分支律的基本理论，重点是离散可分解的情况及其在表示论本身、非交换调和分析中的应用，2.利用Yamabe算子构造伪黎曼流形共形群的正则表示。特别是，我们使用这种机制的最小表示的研究中， ...更多信息有限正交群此外，我们还找到了某些超双曲型方程解的（共形）守恒律。在我们的分析中，分支律在等距群中起着重要的作用（与B.Orsted联合）。3.利用保轨的全纯映射，统一地研究复流形的双全纯变换群的无重数定理。特别地，我们使用这个机器来研究一般线性群的无重性张量积表示。4.在1980年末，我开始了伪黎曼齐性空间的不连续群的研究。在A.Borel的纪念卷中，我发表了一篇关于这一领域的综述文章，并给出了半单对称空间及其切对称空间的余紧不连续群存在的新判据（与T.Yoshino联合）。5.关于这些问题，我在各种国际会议上做了一个小时的特邀演讲，包括ICM 2002，泛非大会2004（全体会议发言），和亚洲大会2005。少