Colored-Descent Representations of Complex Reflection Groups G(r,p,n)

摘要

We study the complex reflection groups G(r,p,n). By considering these groupsas subgroups of the wreath products Z_r wr S_n, 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 flagmajor index, which also has an important role in the decomposition of theserepresentations into irreducibles. A Carlitz type identity relating thecombinatorial parameters with the degrees of the group, is presented.