Study on symplectic space and its representation-theoretic structure

辛空间及其表示理论结构研究

基本信息

批准号：
15540092
负责人：
TAKAKURA Tatsuru
金额：
$ 1.22万
依托单位：
CHUO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

The head investigator Takakura, in collaboration with Taro Suzuki, studied invariants of symplectic quotients for the products of coadjoint orbits of compact Lie groups, and obtained the following results.First, for any simply-connected compact simple Lie group, we derived a general formula which expresses the above invariant as an infinite series. Secondly, for the 3 dimensional special unitary group, we obtained an another formula which expresses the invariant as a finite sum. Both of them are generalizations of earlier results by Takakura for the 2 dimensional special unitary group. Note that the first result may be regarded as an analogue of Witten's volume formula in 2 dimensional Yang-Mills theory. Our method is to reduce, via the fundamental theorem for symplectic quotients, the computation of characteristic numbers to a problem of representation theory of compact Lie groups or complex Lie algebras. More explicitly, we consider the trivial part of the tensor product of irreducib … More le representations and its asymptotic behavior. We can analyze them by the Weyl integration formula and the Verlinde identity for affine Lie algebras.On the other hand, the investigator Miyoshi obtained a result on the smooth representability of the Euler classes of surface bundles.The investigator Ochiai obtained results on non-commutative harmonic oscillator and the connection problem for the Heun differential equation, on polynomials associated with the hypergeometric functions with finite monodromy groups (with M.Yoshida), on absolute derivations and zeta functions (with N.Kurokawa and M.Wakabayashi), on explicit formulas for solutions of some vector-valued hypergeometric differential equations (with M.Fujii), on classification of completely integrable systems with large degree of freedom (with T.Oshima), on intersection theory for located cycles (with K.Mimachi and M.Yoshida), and on number-theoretic property for coefficients of certain polynomial solutions of the Painleve equations (with M.Kaneko). Less

首席调查员高库拉（Takakura）与塔罗铃木（Taro Suzuki）合作，研究了紧凑型谎言组的coadexhighinexhight Orbits产品的符合性报价，并获得了以下结果。首先，对于任何简单紧凑的简单谎言组，我们都表达了上述无效系列的普通公式。其次，对于三维特殊统一组，我们获得了另一个表达不变为有限总和的公式。他们俩都是高仓对2维特别统一组的早期结果的概括。请注意，第一个结果可以被视为在2维杨米尔斯理论中Witten体积公式的类似物。我们的方法是通过对称配额的基本理论来减少特征数量的计算，以指示紧凑型谎言组或复杂谎言代数的代表问题。更明确地，我们考虑了Irreducib的张量产物的琐碎部分……更多的LE代表及其不对称行为。我们可以通过Weyl整合公式和仿生的Verlinde身份进行分析，另一方面，研究人员Miyoshi获得了欧拉表面捆绑包的平稳表示的结果。单型组（与M. Yoshida），在绝对推导和Zeta函数上（具有N.Kurokawa和M.Wakabayashi），在明确的公式上，用于某些矢量价值超几何微分方程的解决方案（与M.Fujii）（具有M.Fujii）（与M.Fujii）（与t.soshima的范围相互作用（与t.oshima）的分类（以及t.soshima）的分类（ K.Mimachi和M.Yoshida），以及用于阵亡的pachleve方程某些多项式溶液系数（带有M.Kaneko）的数字理论特性。较少的