# The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra

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# The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra

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## Description

In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and 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 nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the ""Saturation Conjecture"" for $GL(\ell)$ as a consequence of their solution of the corresponding ""saturation problem"" for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.
Release date Australia
February 15th, 2008
Country of Publication
United States
Illustrations
illustrations
Imprint
American Mathematical Society
ISBN-13
9780821840542
Product ID
2747489

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