The coinvariant algebra $R_n$ is a well-studied $mathfrak{S}_n$-module thatis a graded version of the regular representation of $mathfrak{S}_n$. Using astraightening algorithm on monomials and the Garsia-Stanton basis, Adin,Brenti, and Roichman gave a description of the Frobenius image of $R_n$, gradedby partitions, in terms of descents of standard Young tableaux. Motivated bythe Delta Conjecture of Macdonald polynomials, Haglund, Rhoades, and Shimozonogave an extension of the coinvariant algebra $R_{n,k}$ and an extension of theGarsia-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 $S_{n,k}$.
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