Cherednik algebras and Calogero-Moser cells
Abstract
Using the representation theory of Cherednik algebras at and a Galois covering of the Calogero-Moser space, we define the notions of left, right and two-sided Calogero-Moser cells for any finite complex reflection group. To each Caloger-Moser two-sided cell is associated a Calogero-Moser family, while to each Calogero-Moser left cell is associated a Calogero-Moser cellular representation. We study properties of these objects and we conjecture that, whenever the reflection group is real (i.e. is a Coxeter group), these notions coincide with the one of Kazhdan-Lusztig left, right and two-sided cells, Kazhdan-Lusztig families and Kazhdan-Lusztig cellular representations.
Keywords
Cite
@article{arxiv.1708.09764,
title = {Cherednik algebras and Calogero-Moser cells},
author = {Cédric Bonnafé and Raphaël Rouquier},
journal= {arXiv preprint arXiv:1708.09764},
year = {2022}
}
Comments
330 pages; this is a translated and extended version of arXiv:1302:2720. This new version is largely restructured from the first version