Hall-Littlewood plane partitions and KP

Details Hall-Littlewood plane partitions and KP Hall-Littlewood plane partitions and KP

2008-09-12

arxiv.org/abs/0809.2138v3

Int.Math.Res.Not.2009:2597-2619,2009

Physics

Mathematical Physics

17 pages, minor changes, added a subsection and comments to clarify content, no changes made to conclusions, version to appear

Scientific paper

10.1093/imrn/rnp028

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.

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