Hall-Littlewood plane partitions and KP
Mathematical Physics
2010-03-26 v3 High Energy Physics - Theory
Combinatorics
math.MP
Abstract
MacMahon's classic generating function of random plane partitions, which is related to Schur polynomials, was recently extended by Vuletic to a generating function of weighted plane partitions that is related to Hall-Littlewood polynomials, S(t), and further to one related to Macdonald polynomials, S(t,q). Using Jing's 1-parameter deformation of charged free fermions, we obtain a Fock space derivation of the Hall-Littlewood extension. Confining the plane partitions to a finite s-by-s square base, we show that the resulting generating function, S_{s-by-s}(t), is an evaluation of a tau-function of KP.
Keywords
Cite
@article{arxiv.0809.2138,
title = {Hall-Littlewood plane partitions and KP},
author = {O Foda and M Wheeler},
journal= {arXiv preprint arXiv:0809.2138},
year = {2010}
}
Comments
17 pages, minor changes, added a subsection and comments to clarify content, no changes made to conclusions, version to appear in IMRN