Punctured plane partitions and the q-deformed Knizhnik-Zamolodchikov and Hirota equations

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

de Gier, Jan¹  Pyatov, Pavel^2,3  Zinn-Justin, Paul^4,5,6 

[1] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia

[2] Max Planck Inst Math, D-53111 Bonn, Germany

[3] Joint Inst Nucl Res, Bogoliubov Lab Theoret Phys, Dubna 141980, Moscow Region, Russia

[4] Univ Paris Sud, CNRS, UMR 8626, LPTMS, F-91405 Orsay, France

[5] Univ Paris 06, CNRS, UMR 7589, LPTHE, F-75252 Paris, France

[6] Univ Paris 07, F-75252 Paris, France

关键词: Hirota equation;    qKZ equation;    Plane partitions;    Alternating sign matrices;   

DOI  :  10.1016/j.jcta.2008.11.008

来源: Elsevier

【 摘 要 】

We consider partial sum rules for the homogeneous limit of the solution of the q-deformed Knizhnik-Zamolodchikov equation with reflecting boundaries in the Dyck path representation of the Temperley-Lieb algebra. We show that these partial sums arise in a solution of the discrete Hirota equation, and prove that they are the generating functions of tau(2)-weighted punctured cyclically symmetric transpose complement plane partitions where tau = -(q + q(-1)). in the cases of no or minimal punctures, we prove that these generating functions coincide with tau(2)-enumerations of vertically symmetric alternating sign matrices and modifications thereof. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free