Punctured plane partitions and the q-deformed Knizhnik-Zamolodchikov and Hirota equations
Jan de Gier, Pavel Pyatov, Paul Zinn-Justin
JOURNAL OF COMBINATORIAL THEORY SERIES A | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2009
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 τ2-weighted punctured cyclically symmetric transpose complement plane partitions where τ = - (q + q- 1). In the cases of no or minimal punctures, we prove that these generating functions coincide with τ2-enumerations of vertically symmetric alternating sign matrices and modifications thereof. © 2008 Elsevier Inc. All rights reserved.
Awarded by DFG-RFBR
Awarded by EU
Awarded by ANR
Supported by the DFG-RFBR grants 436 RUS 113/909/0-1(R) and 07-02-91561-a, and by the grant of the Heisenberg-Landau foundation.Supported by EU Marie Curie Research Training Networks "ENRAGE" MRTN-CT-2004-005616, "ENIGMA" MRT-CT-2004-5652, ESF program "MISGAM" and ANR program "GIMP" ANR-05-BI.AN-0029-01.