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We define a combinatorial construction that gives a new subset of the Garsia-Stanton descent monomials whose images under the canonical projection $R_n \to R_\lambda$ descends to a vector space basis of the Garsia-Procesi module $R_\lambda$. As a consequence, our indexing set yields a new formula for the modified Hall-Littlewood polynomials. Our work was discovered whilst searching for a basis of the Garsia-Haiman module, and we discuss partial results in this direction, as well as other connections with the modified Macdonald polynomials $\widetilde{H}_\lambda(X;q,t)$.

This talk serves as Raymond Chou's PhD Exit Seminar talk