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### A Descent Basis for the Garsia-Procesi Module

**Algebra & Discrete Mathematics**

Speaker: | Raymond Chou, UC Davis |

Location: | 1147 MSB |

Start time: | Mon, May 22 2023, 4:10PM |

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