Geodesic
Root games on Grassmannians
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 3, pp. 239-258.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We recall the root game, introduced in [8], which gives a fairly powerful sufficient condition for non-vanishing of Schubert calculus on a generalised flag manifold $G/ B$. We show that it gives a necessary and sufficient rule for non-vanishing of Schubert calculus on Grassmannians. In particular, a Littlewood-Richardson number is non-zero if and only if it is possible to win the corresponding root game. More generally, the rule can be used to determine whether or not a product of several Schubert classes on $Gr _{ l }(\Bbb C ^{ n })$ is non-zero in a manifestly symmetric way. Finally, we give a geometric interpretation of root games for Grassmannian Schubert problems.
Keywords: keywords Schubert calculus, Littlewood-Richardson numbers, grassmannians 
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     title = {Root games on {Grassmannians}},
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Purbhoo, Kevin. Root games on Grassmannians. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 3, pp. 239-258. http://geodesic.mathdoc.fr/item/JAC_2007__25_3_a4/