Abstract
AbstractThe characters of simple Lie algebras are naturally decomposed into lattice-polytope sums. The Brion formula for those polytope sums is remarkably similar to the Weyl character formula. Here we start to investigate if other character formulas have analogs for lattice-polytope sums, by focusing on the Demazure character formulas. Using Demazure operators, we write expressions for the lattice sums of the weight polytopes of rank-2 simple Lie algebras, and the rank-3 algebra A 3.KeywordsLattice polytopesSimple Lie algebrasCharactersDemazure character formula
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