Cellules de Calogero-Moser
Representation Theory
2013-02-13 v1 Algebraic Geometry
Abstract
Using the representation theory of Cherednik algebras at t=0 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.
Cite
@article{arxiv.1302.2720,
title = {Cellules de Calogero-Moser},
author = {Cédric Bonnafé and Raphaël Rouquier},
journal= {arXiv preprint arXiv:1302.2720},
year = {2013}
}
Comments
French, 258 pages