Regularity of Totally Nonnegative Wonderful Compactification
Xuhua He, Kaitao Xie
Source abstract
Let be a split real semisimple group of adjoint type. We prove that the cellular decomposition of the totally nonnegative part of its wonderful compactification is a regular CW complex, confirming a conjecture of Galashin, Karp, and Lam. In particular, the closure of every cell is homeomorphic to a closed ball. The proof combines a Bruhat atlas compatible with total positivity and a CL-labeling of the augmented face poset. The atlas models the strata locally with open Richardson varieties in the flag variety of a larger Kac-Moody group and identifies their totally nonnegative cells.
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