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arXiv · 2010.07114

Closures of O_n orbits in the flag variety for GL_n, II

William M. McGovern
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Abstract

We give a necessary and sufficient condition in terms of pattern avoidance for the conjugates of the bottom vertex in the Bruhat graph attached to an O_n orbit O in the flag variety for GL_n to have degree equal to the rank of this graph as a poset, showing that this condition is equivalent to the rational smoothness of the closure of O. We also give a necessary and sufficient condition in terms of pattern avoidance for the closure of O to be smooth.

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William M. McGovern. 2020-10-12. Closures of O_n orbits in the flag variety for GL_n, II. https://arxiv.org/abs/2010.07114

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