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PreprintCC BY 4.0arXiv

Regularity of Totally Nonnegative Wonderful Compactification

  • Xuhua He
  • Kaitao Xie
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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.

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Cite

BibTeXRIS
BibTeX
@misc{he2026regularity,
  title = {{Regularity of Totally Nonnegative Wonderful Compactification}},
  author = {Xuhua He and Kaitao Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16332},
  eprint = {2610.16332},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16332},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Regularity of Totally Nonnegative Wonderful Compactification
AU  - Xuhua He
AU  - Kaitao Xie
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16332
UR  - https://arxiv.org/abs/2610.16332
AB  - 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.
ER  -