Cellules de Calogero-Moser

Cédric Bonnafé (1) , Raphaël Rouquier (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
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.

Mots clés: complex reflection group; Cherednik algebras; Calogero-Moser space; Verma modules; cells; families

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Cédric Bonnafé, Raphaël Rouquier. Cellules de Calogero-Moser. 2013. ⟨hal-00787349⟩