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

TL;DR

This paper conjectures a novel link between solutions of the quantum Knizhnik-Zamolodchikov equation and q-enumerations of symmetric plane partitions, suggesting deep combinatorial and algebraic connections.

Contribution

It introduces a new conjecture connecting quantum algebra solutions with combinatorial enumeration of symmetric plane partitions.

Findings

Proposes a conjecture relating KZ equation solutions to plane partition enumeration.

Highlights potential algebraic-combinatorial correspondence in symmetric structures.

Suggests avenues for future proof and exploration of the conjecture.

Abstract

We present a new conjecture relating the minimal polynomial solution of the level-one $U_q(\frak{sl}(2))$ 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.