Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices
P. Di Francesco 1, Paul Zinn-Justin 2
Theoretical and Mathematical Physics 154 (2008) 331-348
We present multiresidue formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco '06] connecting the above to generating polynomials for weighted Totally Symmetric Self-Complementary Plane Partitions. We reduce the corresponding conjectures to a single integral identity, yet to be proved.
- 1. Service de Physique Théorique (SPhT),
CNRS : URA2306 – CEA : DSM/SPHT - 2. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
