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arXiv · 0712.3584

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

Jan de Gier·Pavel Pyatov·Paul Zinn-Justin
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Abstract

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. 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.

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Jan de Gier, Pavel Pyatov, Paul Zinn-Justin. 2007-12-21. Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations. https://doi.org/10.1016/j.jcta.2008.11.008

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