Yamanouchi bitableaux interpretation of Kronecker coefficients

Prove that each Kronecker coefficient is equal to the number of lexicographic bitableaux of the prescribed shape and weights whose two reading words satisfy the required pair of Yamanouchi conditions.

Background

The paper introduces lexicographic bitableaux as combinatorial objects intended to model the Kronecker coefficients, which are multiplicities in tensor products or restrictions of representations. The conjecture proposes that imposing suitable Yamanouchi conditions on two reading words of a bitableau will isolate the highest-weight elements corresponding to the Kronecker coefficients.

The authors explain that they currently have a satisfactory procedure for extracting only one of the two required reading words. Consequently, identifying the second reading word is the central unresolved step in realizing the proposed combinatorial interpretation.