Séminaire Lotharingien de Combinatoire, 84B.31 (2020), 12 pp.

Pavel Galashin, Steven N. Karp and Thomas Lam

Regularity Theorem for Totally Nonnegative Flag Varieties

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.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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