Enumerating projective reflection groups


Projective reflection groups have been recently defined 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 reflection groups of type G(r, p, n). In this paper we define some statistics analogous to
descent number and major index over the projective reflection 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.

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