Descent-cycling in Schubert calculus

Details Descent-cycling in Schubert calculus Descent-cycling in Schubert calculus

2000-09-11

arxiv.org/abs/math/0009112v1

Experiment. Math. 10 (2001), no. 3, 345--353

Mathematics

Combinatorics

10 pages, 2 figures, see also http://www.math.berkeley.edu/~allenk/java/DCApplet.html

Scientific paper

We prove two lemmata about Schubert calculus on generalized flag manifolds G/B, and in the case of the ordinary flag manifold GL_n/B we interpret them combinatorially in terms of descents, and geometrically in terms of missing subspaces. One of them gives a symmetry of Schubert calculus that we christen_descent-cycling_. Computer experiment shows that these lemmata suffice to determine all of GL_n Schubert calculus through n=5, and 99.97%+ at n=6. We use them to give a quick proof of Monk's rule. The lemmata also hold in equivariant (``double'') Schubert calculus for Kac-Moody groups G.

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