Mirkovic-Vilonen cycles and polytopes

• 成果类型: Article
• 署名作者: Kamnitzer, Joel
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.245
• 发表日期: 2010
• 页码: 245-294
• 关键词: canonical bases

摘要

We give an explicit description of the Mirkovie-Vilonen cycles on the affine Grassmannian for arbitrary complex reductive groups. We also give a combinatorial characterization of the MV polytopes. We prove that a polytope is an MV polytope if and only if it is a lattice polytope whose defining hyperplanes are parallel to those of the Weyl polytopes and whose 2-faces are rank 2 MV polytopes. As an application, we give a bijection between Lusztig's canonical basis and the set of MV polytopes.