Character formulas and descent representations for colored permutation groups

The quasisymmetric generating function of an inverse descent class is known to be symmetric, and there is a corresponding descent representation of the symmetric group. This result was generalized to products of inverse descent classes and Schur-positive sets of permutations by Elizalde and Roichman (2017), and to signed permutations by Adin, Athanasiadis, Elizalde and Roichman (2017).

In this talk we present colored extensions of these two results. Proof ingredients include a new notion of colored ribbon, a colored version of Stanley's shuffling theorem, and a character formula for colored descent representations.

All relevant notions will be explained in the talk.