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

Introduction Roots and Coxeter groups The first three algebra problems and the parameter spaces $\Sigma$ for $K\backslash \overline{G}/K$ The existence of polygonal linkages and solutions to the algebra problems Weighted configurations, stability and the relation to polygons Polygons in Euclidean buildings and the generalized invariant factor problem The existence of fixed vertices in buildings and computation of the saturation factors for reductive groups The comparison of problems Q3 and Q4 Appendix A. Decomposition of tensor products Appendix. Bibliography