Totally Symmetric Self-Complementary Plane Partitions and Quantum Knizhnik-Zamolodchikov equation: a conjecture

We present a new conjecture relating the minimal polynomial solution of the level-one $U_q(\mathfrak{s}\mathfrak{l}(2))$ quantum Knizhnik-Zamolodchikov equation for generic values of $q$ in the link pattern basis and some $q$-enumeration of Totally Symmetric Self-Complementary Plane Partitions.