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We present multiresidue formulae for partial sums in the basis of linkpatterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantumKnizhnik--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 TotallySymmetric Self-Complementary Plane Partitions. We reduce the correspondingconjectures to a single integral identity, yet to be proved.

Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices