3 problems

Frequency-parametrization conjecture. In the finite-rank case, these limits are finite for every $i$, and conversely, for every $\lambda=(\lambda_1,\ldots,\lambda_d)\in\mathcal{C}$…

Frequency-uniqueness conjecture. For general Gelfand–Tsetlin type graphs, central measures are uniquely determined by their limiting frequencies.

Frequency-uniqueness conjecture. For homogeneous Gelfand–Tsetlin type graphs, the frequencies uniquely determine an ergodic central measure.