Open boundary Quantum Knizhnik-Zamolodchikov equation and the weighted enumeration of Plane Partitions with symmetries

Details Open boundary Quantum Knizhnik-Zamolodchikov equation and the weighted enumeration of Plane Partitions with symmetries Open boundary Quantum Knizhnik-Zamolodchikov equation and the weighted enumeration of Plane Partitions with symmetries

2006-11-07

arxiv.org/abs/math-ph/0611012v2

Physics

Mathematical Physics

27 pages, uses lanlmac, epsf and hyperbasics, minor revisions

Scientific paper

10.1088/1742-5468/2007/01/P01024

We propose new conjectures relating sum rules for the polynomial solution of the qKZ equation with open (reflecting) boundaries as a function of the quantum parameter $q$ and the $\tau$-enumeration of Plane Partitions with specific symmetries, with $\tau=-(q+q^{-1})$. We also find a conjectural relation \`a la Razumov-Stroganov between the $\tau\to 0$ limit of the qKZ solution and refined numbers of Totally Symmetric Self Complementary Plane Partitions.

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