Cactus groups and Lusztig's asymptotic algebra
Representation Theory
2024-09-02 v1
Abstract
We construct a morphism from the cactus group associated with a Coxeter group to the group of invertible elements of Lusztig's asymptotic algebra. This relates to the cactus group action on elements of Coxeter groups defined by Losev and Bonnaf\'e and we propose a conjecture on how to fully recover those actions.
Keywords
Cite
@article{arxiv.2408.16922,
title = {Cactus groups and Lusztig's asymptotic algebra},
author = {Raphael Rouquier and Noah White},
journal= {arXiv preprint arXiv:2408.16922},
year = {2024}
}