Cherednik algebras and Calogero-Moser cells

Cédric Bonnafé (1) , Raphaël Rouquier (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Department of Mathematics [UCLA]

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.

Domaines: Théorie des représentations [math.RT]

Cédric Bonnafé, Raphaël Rouquier. Cherednik algebras and Calogero-Moser cells. 2022. ⟨hal-01579418v3⟩