The combinatorics of quiver representations

摘要: We give a description of faces all codimensions for the cones weights rings semi-invariants quivers. For triple flag quiver and codimension 1 this reduces to result Knutson-Tao-Woodward on facets Klyachko cone. new applications Littlewood-Richardson coefficients, including product formula LR-coefficients corresponding triples partitions lying wall systematically review develop necessary methods (exceptional Schur sequences, orthogonal categories, semi-stable decompositions, GIT quotients quivers). In Appendix we include version Belkale's geometric proof Fulton's conjecture that works arbitrary