Regularity theorem for totally nonnegative flag varieties

Galashin, Pavel; Karp, Steven; Lam, Thomas

doi:10.1090/jams/983

Regularity theorem for totally nonnegative flag varieties
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by Pavel Galashin, Steven N. Karp and Thomas Lam

J. Amer. Math. Soc. 35 (2022), 513-579

DOI: https://doi.org/10.1090/jams/983

Published electronically: September 24, 2021

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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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