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

William M. McGovern; Peter E. Trapa

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arXiv · 0904.4493

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

William M. McGovern·Peter E. Trapa

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Abstract

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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BibTeX RIS

William M. McGovern, Peter E. Trapa. 2012-03-19. Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety. https://arxiv.org/abs/0904.4493

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