Seminar Event Detail


Date:  Friday, April 17, 2015
Location:  3866 East Hall (4:10 PM to 5:00 PM)

Title:  Combinatorics of the q,t-symmetry relation in Macdonald polynomials

Abstract:   The Macdonald polynomials H_mu(X;q,t) are certain symmetric functions in the variables X={x_1,x_2,...} with coefficients in Q(q,t). Arising naturally in the context of the geometry of the Hilbert scheme of points in the plane, these polynomials also exhibit a beautiful symmetry relation in the variables q and t. We investigate the combinatorics of this symmetry relation in light of the combinatorial formula for the Macdonald polynomials discovered by Haglund, Haiman, and Loehr in 2004. The relation is a strict generalization of the well-known equidistribution of the Mahonian statistics inv and maj on permutations.


Speaker:  Maria Monks Gillespie
Institution:  U. California at Berkeley

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