Polygons in symmetric spaces and buildings with applications to algebra

这个项目属于曲率有界的度量空间的框架内。它涉及高阶非正曲线空间的几何，即非紧型对称空间和欧几里得建筑的几何。我们将研究一些基本问题，如多边形边长的限制，以及与此相关的一般几何结构理论的进一步发展。在研究方法上，主要是比较几何、建筑理论和李理论，此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和方法都是几何问题，但它在代数问题中也有重要的应用，例如H·Weyl提出的求和问题的特征值和表示论中的张量积分解问题。

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.