The Combinatorics of Quiver Representations
表示论
2011-11-09 v2 交换代数
代数几何
组合数学
摘要
We give a description of faces of all codimensions for the cones of weights of rings of semi-invariants of quivers. For a triple flag quiver and faces of codimension 1 this reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically review and develop the necessary methods (exceptional and Schur sequences, orthogonal categories, semi-stable decompositions, GIT quotients for quivers). In the Appendix we include a version of Belkale's geometric proof of Fulton's conjecture that works for arbitrary quivers.
引用
@article{arxiv.math/0608288,
title = {The Combinatorics of Quiver Representations},
author = {Harm Derksen and Jerzy Weyman},
journal= {arXiv preprint arXiv:math/0608288},
year = {2011}
}
备注
63 pages