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Cells, cacti, and the asymptotic algebra
Abstract
We prove that the action of the cactus group on a Coxeter group defined by Losev and Bonnafé can be realised as an action on the asymptotic algebra of the Hecke algebra, thus resolving a conjecture of Rouquier and White. We prove this in the setting of general (potentially unequal) parameters, conditional on Lusztig's conjectures P1-P15, which are known to hold in the equal parameter case.
Related
- Asymptotic Behavior of Distance near the Origin Between Two Elements of the Semigroup in a Banach Algebra
- Lusztig's asymptotic algebra and a cell factorisation for the second lowest two-sided cell in type B̃n
- Additive quasi-isometries and cacti
- Subregular affine cells and the level −1 vertex algebra of type D
- Two-distance and list-two-distance coloring of cacti: the subcubic case and the C5 obstruction
BibTeX
@misc{santos2026cells,
title = {{Cells, cacti, and the asymptotic algebra}},
author = {F. Dos Santos and J. Parkinson},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07439},
eprint = {2611.07439},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07439},
}
RIS
TY - UNPB
TI - Cells, cacti, and the asymptotic algebra
AU - F. Dos Santos
AU - J. Parkinson
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07439
UR - https://arxiv.org/abs/2611.07439
AB - We prove that the action of the cactus group on a Coxeter group defined by Losev and Bonnafé can be realised as an action on the asymptotic algebra of the Hecke algebra, thus resolving a conjecture of Rouquier and White. We prove this in the setting of general (potentially unequal) parameters, conditional on Lusztig's conjectures P1-P15, which are known to hold in the equal parameter case.
ER -