ENUMERATING PROJECTIVE REFLECTION GROUPS

Riccardo Biagioli (1) , Fabrizio Caselli (1)

1 ICJ - Institut Camille Jordan

Projective re ection groups have been recently dened by the second author. They include a special class of groups denoted G(r; p; s; n) which contains all classical Weyl groups and more generally all the complex re ection groups of type G(r; p; n). In this paper we dene some statistics analogous to descent number and major index over the projective re ection groups G(r; p; s; n), and we compute several generating functions concerning these parameters. Some aspects of the representation theory of G(r; p; s; n), as distribution of one-dimensional characters and computation of Hilbert series of invariant algebras, are also treated.

Domaines: Combinatoire [math.CO]

Riccardo Biagioli, Fabrizio Caselli. ENUMERATING PROJECTIVE REFLECTION GROUPS. 2011. ⟨hal-00557536⟩