Combinatorial formulas connected to diagonal harmonics and Macdonald polynomials |
Posted on:2010-03-18 | Degree:Ph.D | Type:Dissertation |
University:University of Pennsylvania | Candidate:Yoo, Meesue | Full Text:PDF |
GTID:1440390002977711 | Subject:Mathematics |
Abstract/Summary: | |
We study bigraded Sn-modules introduced by Garsia and Haiman as an approach to prove the Macdonald positivity conjecture. We construct a combinatorial formula for the Hilbert series of Garsia-Haiman modules as a sum over standard Young tableaux, and provide a bijection between a group of fillings and the corresponding standard Young tableau in the hook shape case. This result extends the known property of Hall-Littlewood polynomials by Garsia and Procesi to Macdonald polynomials.;We also study the integral form of Macdonald polynomials and construct a combinatorial formula for the coefficients in the Schur expansion in the one-row case and the hook shape case. |
Keywords/Search Tags: | Macdonald, Combinatorial, Polynomials |
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