Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety

Details Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety

2009-04-29

arxiv.org/abs/0904.4493v4

Mathematics

Representation Theory

20 pages, 3 figures. Minor revisions (corrected typos and incorporated updates from arXiv:0905.0127v2)

Scientific paper

We give a pattern avoidance criterion to classify the orbits of Sp(p,C) x
Sp(q,C) (resp. GL(n,C)) on the flag variety of type C_{p+q} (resp. D_n) with
rationally smooth closure. We show that all such orbit closures fiber (with
smooth fiber) over a smaller flag variety, and hence are in fact smooth. In
addition we prove that the classification is insensitive to isogeny.

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