  The coinvariant algebra $R_n$ is a well-studied $\mathfrak{S}_n$-module that
is a graded version of the regular representation of $\mathfrak{S}_n$. Using a
straightening algorithm on monomials and the Garsia-Stanton basis, Adin,
Brenti, and Roichman gave a description of the Frobenius image of $R_n$, graded
by partitions, in terms of descents of standard Young tableaux. Motivated by
the Delta Conjecture of Macdonald polynomials, Haglund, Rhoades, and Shimozono
gave an extension of the coinvariant algebra $R_{n,k}$ and an extension of the
Garsia-Stanton basis. Chan and Rhoades further extend these results from
$\mathfrak{S}_n$ to the complex reflection group $G(r,1,n)$ by defining a
$G(r,1,n)$ module $S_{n,k}$ that generalizes the coinvariant algebra for
$G(r,1,n)$. We extend the results of Adin, Brenti, and Roichman to $R_{n,k}$
and $S_{n,k}$.
