Regularity theorem for totally nonnegative flag varieties
Combinatorics
2023-07-04 v3 Algebraic Geometry
Geometric Topology
Representation Theory
Abstract
We show that the totally nonnegative part of a partial flag variety (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.
Keywords
Cite
@article{arxiv.1904.00527,
title = {Regularity theorem for totally nonnegative flag varieties},
author = {Pavel Galashin and Steven N. Karp and Thomas Lam},
journal= {arXiv preprint arXiv:1904.00527},
year = {2023}
}
Comments
63 pages, 2 figures; v2: Minor changes; v3: Final version to appear in J. Amer. Math. Soc