Regularity theorem for totally nonnegative flag varieties

By Pavel Galashin, Steven N. Karp, Thomas Lam. Journal of The American Mathematical Society, 2019

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

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