A polynomiality property for Littlewood-Richardson coefficients
Journal of Combinatorial Theory Series A
Combinatorics and geometry of Littlewood-Richardson cones
European Journal of Combinatorics - Special issue on combinatorics and representation theory
Factorisation of Littlewood--Richardson coefficients
Journal of Combinatorial Theory Series A
Reductions of Young Tableau Bijections
SIAM Journal on Discrete Mathematics
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A new combinatorial expression is given for the dimension of the space of invariants in the tensor product of three irreducible finite dimensional sl(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 “universal” 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 sl(r + 1)-module.