Signed Mahonian on parabolic quotients of colored permutation groups

We study the generating polynomial of flag major index with each one-dimensional character, called signed Mahonian polynomial, over colored permutation group, wreath product a cyclic group symmetric group. Using insertion lemma Han and Haglund–Loehr–Remmel extension established by Eu et al., we derive quotients parabolic subgroups for variety systems coset representatives in terms subsequence restrictions. This generalizes related work due to Caselli as well al. As byproduct, formula that Biagioli's result about on even groups.