Abstract
We define a collection of polytopes associated to a semisimple group $\mathsf {G}$. Weight multiplicities and tensor product multiplicities may be computed as the number of such polytopes fitting in a certain region. The polytopes are defined as moment map images of algebraic cycles discovered by I. Mirković and K. Vilonen. These cycles are a canonical basis for the intersection homology of (the closures of the strata of) the loop Grassmannian.
Citation
Jared E. Anderson. "A polytope calculus for semisimple groups." Duke Math. J. 116 (3) 567 - 588, 15 February 2003. https://doi.org/10.1215/S0012-7094-03-11636-1
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