Year: 2026
Type: preprint
Abstract: Let $G$ 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.
Source: arXiv (Cornell University)
Authors: He, Xuhua, Xie, Kaitao
Institution: University of Hong Kong
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221832530