PreprintCC BY-NC-SA 4.0arXiv
Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts
Abstract
Demazure weaves are combinatorial representations of maps between Bott--Samelson cells and have been used to construct cluster structures on braid varieties. We show the compatibility of these maps and the resulting cluster structures with the standard Poisson structure on the Bott--Samelson variety. Adding frayed strands to Demazure weaves, we further construct Poisson compatible cluster structures on other affine charts of the Bott--Samelson variety in a manner that transition functions across charts become rational quasi-cluster. The mutation sequences we construct for these quasi-cluster morphisms are closely related to those of Ménard for open Richardson seeds.
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BibTeX
@misc{cheah2026frayed,
title = {{Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts}},
author = {Jon Cheah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.05823},
eprint = {2606.05823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.05823},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts
AU - Jon Cheah
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2606.05823
UR - https://arxiv.org/abs/2606.05823
AB - Demazure weaves are combinatorial representations of maps between Bott--Samelson cells and have been used to construct cluster structures on braid varieties. We show the compatibility of these maps and the resulting cluster structures with the standard Poisson structure on the Bott--Samelson variety. Adding frayed strands to Demazure weaves, we further construct Poisson compatible cluster structures on other affine charts of the Bott--Samelson variety in a manner that transition functions across charts become rational quasi-cluster. The mutation sequences we construct for these quasi-cluster morphisms are closely related to those of Ménard for open Richardson seeds.
ER -