2003/05/21 by Jared E. Anderson, Anderson, Jared E., M. G. Kogan +2
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0305297
updated title and introduction
openalex publication_date 2003/05/21 · arxiv created 2003/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.