arXiv Open Access 2022

Total positivity in twisted product of flag varieties

Huanchen Bao Xuhua He

Lihat Sumber

Abstrak

We show that the totally nonnegative part of the twisted product of flag varieties of a Kac-Moody group admits a cellular decomposition, and the closure of each cell is a topological manifold with boundary. We also establish explicit parameterizations of each totally positive cell. In the special cases of double flag varieties and braid varieties, we show that the totally nonnegative parts are regular CW complexes homeomorphic to closed balls. Moreover, we prove that the link of any totally nonnegative double Bruhat cell in a reductive group is a regular CW complex homeomorphic to a closed ball, solving an open problem of Fomin and Zelevinsky.

Topik & Kata Kunci

math.RT math.AG math.CO math.GN

Penulis (2)

Huanchen Bao

Xuhua He

Format Sitasi

APA MLA BibTeX

Bao, H., He, X. (2022). Total positivity in twisted product of flag varieties. https://arxiv.org/abs/2211.11168

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓