Colored-descent representations of complex reflection groups G(r,p,n)
We study the complex reflection groups G(r,p,n). By considering
these groups as subgroups of the wreath products of
Zr and Sn
and by using Clifford theory, we define combinatorial
parameters and descent representations of G(r,p,n), previously
known for classical Weyl groups. One of these parameters is the
flag major index, which also has an important role in the
decomposition of these representations into irreducibles. A
Carlitz type identity relating the combinatorial parameters with
the degrees of the group, is presented.