Polygons in symmetric spaces and buildings with applications to algebra

这个项目属于度量空间的框架与曲率有界以上。它涉及的几何非积极弯曲空间的更高的秩，即对称空间的非紧型和欧几里得建筑。我们将研究一些基本问题，如多边形边长的限制，并在此基础上进一步发展一般几何结构理论。至于方法，比较几何，建筑理论和李理论在我们的调查中发挥了主要作用，除此之外，还有辛几何和代数几何思想的影响。虽然我们主要感兴趣的问题以及方法是几何的，但它在代数问题中有重要的应用，例如和的特征值问题可以追溯到H。Weyl与表示论中张量积的分解问题。

This project belongs within the framework of metric spaces with curvature bounded above. It concerns the geometry of nonpositively curved spaces of higher rank, that is, of symmetric spaces of noncompact type and Euclidean buildings. We will study some basic questions such as restrictions on the side lengths of polygons and in relation with this develop further the general geometric structure theory. As for the methods, comparison geometry, building theory and Lie theory play the main role in our investigations, and apart from this there is influence by ideas from symplectic geometry and algebraic geometry. Although the questions we are mainly interested in as well as the methods are geometric, there are serious applications to algebraic problems, such as Eigenvalues of a Sum problem going back to H. Weyl and the Decompositon of Tensor Products problem in representation theory.