A kicking basis for the two-column Garsia-Haiman modules
Combinatorics
2009-05-15 v1 Representation Theory
Abstract
In the early 1990s, Garsia and Haiman conjectured that the dimension of the Garsia-Haiman module 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 the module 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 Garsia-Haiman modules indexed by a partition with at most two columns.
Cite
@article{arxiv.0905.2333,
title = {A kicking basis for the two-column Garsia-Haiman modules},
author = {Sami Assaf and Adriano Garsia},
journal= {arXiv preprint arXiv:0905.2333},
year = {2009}
}
Comments
14 pages, 7 figures, to appear in DMTCS as part of the conference proceedings for FPSAC 2009