Mathematical Sciences: Integral Geometry and Analysis on Affine Symmetric Spaces

Gindikin将调查多维问题， 仿射对称空间的积分几何与分析。 的 该项目的第一部分将是构建本地反演 公式，并将它们与李的表示理论联系起来 组 建议的第二部分将考虑分析 在齐次锥和Siegel域上， 从表现中发展明确的结果实现 理论，包括Plancherel测度和球函数。 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身和理论物理学，特别是 量子力学和基本粒子物理学。

Gindikin will investigate multidimensional problems in integral geometry and analysis on affine symmetric spaces. The first part of this project will be to construct local inversion formulas and to relate them to the representation theory of Lie groups. The second part of the proposal will consider analysis on homogeneous cones and Siegel domains with an aim towards developing explicit realizations of results from representation theory, including Plancherel measure and spherical functions. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself and theoretical physics, especially quantum mechanics and elementary particle physics.