Hall-Littlewood Plane Partitions and KP
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Publication:5191255
DOI10.1093/IMRN/RNP028zbMATH Open1182.05004arXiv0809.2138OpenAlexW3099291129MaRDI QIDQ5191255
Author name not available (Why is that?)
Publication date: 29 July 2009
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/0809.2138
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