DMTCS Proceedings, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

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A kicking basis for the two column Garsia-Haiman modules

S. Assaf, A. Garsia


In the early 1990s, Garsia and Haiman conjectured that the dimension of the Garsia-Haiman module Rµ is n!, and they showed that the resolution of this conjecture implies the Macdonald Positivity Conjecture. Haiman proved these conjectures in 2001 using algebraic geometry, but the question remains to find an explicit basis for Rµ which would give a simple proof of the dimension. Using the theory of Orbit Harmonics developed by Garsia and Haiman, we present a "kicking basis" for Rµ when µ has two columns.

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