A polytope combinatorics for semisimple groups
Algebraic Geometry
2007-05-23 v1 Combinatorics
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0110225,
title = {A polytope combinatorics for semisimple groups},
author = {Jared E. Anderson},
journal= {arXiv preprint arXiv:math/0110225},
year = {2007}
}
Comments
17 pages, 10 figures