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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