K-orbits on G/B and Schubert constants for pairs of signed shuffles in types C and D

Details K-orbits on G/B and Schubert constants for pairs of signed shuffles in types C and D K-orbits on G/B and Schubert constants for pairs of signed shuffles in types C and D

2011-09-12

arxiv.org/abs/1109.2574v2

Mathematics

Combinatorics

23 pages. Corrected typos

Scientific paper

We give positive descriptions for certain Schubert structure constants $c_{u,v}^w$ for the full flag variety in Lie types $C$ and $D$. This is accomplished by first observing that a number of the $K=GL(n,\C)$-orbit closures on these flag varieties coincide with Richardson varieties, and then applying a theorem of M. Brion on the decomposition of such an orbit closure in the Schubert basis in terms of paths in the weak order graph.

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