Root games on Grassmannians |
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Authors: | Kevin Purbhoo |
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Institution: | (1) Department of Mathematics, University of British Columbia, 1984 Mathematics Rd., Vancouver, BC, V6T 1Z2, Canada |
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Abstract: | 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
(ℂ
n
) is non-zero in a manifestly symmetric way. Finally, we give a geometric interpretation of root games for Grassmannian Schubert
problems.
Research partially supported by an NSERC scholarship. |
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Keywords: | Schubert calculus Littlewood-Richardson numbers Grassmannians |
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