Total positivity in twisted product of flag varieties
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916134423363584 |
|---|---|
| author | Bao, Huanchen He, Xuhua |
| author_facet | Bao, Huanchen He, Xuhua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_11168 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Total positivity in twisted product of flag varieties Bao, Huanchen He, Xuhua Representation Theory Algebraic Geometry Combinatorics General Topology 14M15, 20G44, 15B48 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. |
| title | Total positivity in twisted product of flag varieties |
| topic | Representation Theory Algebraic Geometry Combinatorics General Topology 14M15, 20G44, 15B48 |
| url | https://arxiv.org/abs/2211.11168 |