对称空间和建筑物中的广义三角不等式及其代数应用
The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra
摘要：
本文将我们关于Cartan子空间、对称空间和建筑物中多边形几何的结果应用于代数群理论中的四个问题。其中两个问题是寻找特征值约束问题的推广（分别是）。奇异值）的总和（分别为当每个被加数（因子）的特征值（奇异值）固定时，另外两个问题是关于Q上分裂约化代数群及其复Langlands对偶的Hecke环和表示环的结构常数的计算。本文给出了GL（m）的“饱和猜想”的一个新的证明，作为我们解决Q上所有分裂约化代数群的Hecke结构常数的“饱和问题”的结果.
英文摘要：
In this paper we apply our results on the geometry of polygons in Cartan subspaces, symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the computation of the structure constants of the Hecke and representation rings associated with a split reductive algebraic group over Q and its complex Langlands' dual. We give a new proof of the ``Saturation Conjecture'' for GL(m) as a consequence of our solution of the corresponding ``saturation problem'' for the Hecke structure constants for all split reductive algebraic groups over Q.
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