Geodesic
Triple multiplicities for $s\ell (r+1)$ and the spectrum of the exterior algebra of the adjoint representation
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 1, pp. 7-22.

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Summary: A new combinatorial expression is given for the dimension of the space of invariants in the tensor product of three irreducible finite dimensional $s$l(r + 1)-modules (we call this dimension the triple multiplicity). This expression exhibits a lot of symmetries that are not clear from the classical expression given by the Littlewood-Richardson rule. In our approach the triple multiplicity is given as the number of integral points of the section of a certain $ldquo$universal $rdquo$ polyhedral convex cone by a plane determined by three highest weights. This allows us to study triple multiplicities using ideas from linear programming. As an application of this method, we prove a conjecture of B. Kostant that describes all irreducible constituents of the exterior algebra of the adjoint $s$l(r + 1)-module.
Keywords: tensor product multiplicities, systems of linear inequalities 
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     title = {Triple multiplicities for $s\ell (r+1)$ and the spectrum of the exterior algebra of the adjoint representation},
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Berenstein, A.D.; Zelevinsky, A.V. Triple multiplicities for $s\ell (r+1)$ and the spectrum of the exterior algebra of the adjoint representation. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 1, pp. 7-22. http://geodesic.mathdoc.fr/item/JAC_1992__1_1_a4/