A kicking basis for the two column Garsia-Haiman modules by Sami Assaf, Adriano Garsia

“…$, 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 $R_{\mu}$ which would give a simple proof of the dimension. …”
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Wreath Macdonald polynomials and the categorical McKay correspondence by Bezrukavnikov, Roman, Finkelberg, Michael, Vologodsky, Vadim

“…Mark Haiman has reduced Macdonald Positivity Conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjectures where the symmetric group is replaced by the wreath product Sn[subscript ⋉](Z/rZ)[superscript n]. …”
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