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

@inproceedings{Mcgovern2009PatternAA, title={Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety}, author={William Montgomery Mcgovern and Peter E. Trapa}, year={2009} }

Abstract We give a pattern avoidance criterion to classify the orbits of Sp ( p , C ) × 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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## Combinatorial results on (1,2,1,2)-avoiding $GL(p,\mathbb{C}) \times GL(q,\mathbb{C})$-orbit closures on $GL(p+q, \mathbb{C})/B$

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