Duke Mathematical Journal

A polytope calculus for semisimple groups

Jared E. Anderson

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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.

Article information

Duke Math. J. Volume 116, Number 3 (2003), 567-588.

First available in Project Euclid: 26 May 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20G05: Representation theory
Secondary: 14L99: None of the above, but in this section


Anderson, Jared E. A polytope calculus for semisimple groups. Duke Math. J. 116 (2003), no. 3, 567--588. doi:10.1215/S0012-7094-03-11636-1. http://projecteuclid.org/euclid.dmj/1085598302.

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