Mirkovic-Vilonen圈与A型多面体
Mirkovic-Vilonen cycles and polytopes in type A
摘要：
本文研究了A型代数圈（MV-圈）。Mirković和K. Vilonen [MV].特别地，我们将循环格拉斯曼划分为光滑的片段，使得MV-循环是它们的闭包。我们使用A型循环格拉斯曼的格子模型明确地描述每一片中的点。该分区在余权的作用下是不变的，并且在此作用之前，这些块由Kostant参数集参数化。这种描述的MV-圈，使我们能够证明的主要结果的文件：计算的矩映射图像的MV-圈（MV-多面体），通过确定每个多面体的顶点。
英文摘要：
We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirković and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to this action, the pieces are parametrized by the Kostant parameter set. This description of MV-cycles allows us to prove the main result of the paper: the computation of the moment map images of MV-cycles (MV-polytopes) by identifying the vertices of each polytope.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
