2001/10/19 by Jared E. Anderson, Anderson, Jared E. · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Finite Group Theory Research #math.AG #math.CO #math.RT
paper · pdf · doi:10.48550/arxiv.math/0110225
17 pages, 10 figures
arxiv created 2001/10/19 · arxiv updated 2009/11/30
Mirkovic and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties are a collection of polytopes, and they may be used to compute weight multiplicities and tensor product multiplicities for representations of a semisimple group. The polytopes are explicitly described for a few low rank groups.