Date: Friday, September 08, 2017
Location: 4088 East Hall (4:10 PM to 5:00 PM)
Title: Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture
Abstract: Consider the action of the symmetric group S_n on the polynomial ring Q[x_1, ..., x_n] by variable permutation. The coinvariant algebra R_n is the graded S_nmodule obtained by modding out Q[x_1, \dots, x_n] by the ideal generated by S_n$invariant polynomials with vanishing constant term. The algebraic properties of R_n are governed by the combinatorial properties of permutations. We will introduce and study a family of graded S_nmodules R_{n,k} which reduce to the coinvariant algebra when k = n. The algebraic properties of the R_{n,k} are governed by ordered set partitions of {1, 2, \dots, n} with k blocks. We will generalize results of E. Artin, GarsiaStanton, Chevalley, and LusztigStanley from R_n to R_{n,k}. The modules R_{n,k} are related to the "Delta Conjecture" in the theory of Macdonald polynomials. Joint with Jim Haglund and Mark Shimozono.
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Speaker: Brendon Rhoades
Institution: UC San Diego
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