Root games on Grassmannians

Details Root games on Grassmannians Root games on Grassmannians

2003-10-08

arxiv.org/abs/math/0310103v3

Journal of Algebraic Combinatorics, 25 (2007) no. 3, 239-258

Mathematics

Combinatorics

21 pages, 5 figures. Final version

Scientific paper

We recall the root game, introduced in an earlier paper, 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(n) is non-zero in a manifestly symmetric way. Finally, we give a geometric interpretation of root games for Grassmannian Schubert problems.

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