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arXiv · 1904.00527

Regularity theorem for totally nonnegative flag varieties

Pavel Galashin·Steven N. Karp·Thomas Lam
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Abstract

We show that the totally nonnegative part of a partial flag variety $G/P$ (in the sense of Lusztig) is a regular CW complex, confirming a conjecture of Williams. In particular, the closure of each positroid cell inside the totally nonnegative Grassmannian is homeomorphic to a ball, confirming a conjecture of Postnikov.

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Pavel Galashin, Steven N. Karp, Thomas Lam. 2021-04-12. Regularity theorem for totally nonnegative flag varieties. https://doi.org/10.1090/jams%2F983

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