Monomial-product property for multi-$t$ Macdonald coefficients

Let

$$\tilde H_\mu(X;q,{\bf t})=\sum_\lambda \tilde K[q,{\bf t}]s_\lambda$$

and write each coefficient as

$$\tilde K[q,{\bf t}]=\sum_{k,\alpha}c_{k,\alpha}q^k{\bf t}^\alpha.$$

For cells $(i,j)$ of the Ferrers diagram of $bc$, let $d_bc$ be the number of standard tableaux of shape $bc$ in which $2$ is above $1$, and set $t_0=1$.

Monomial-product conjecture.

$$\prod_{k,\alpha}(q^kT^\alpha)^{c_{k,\alpha}}=\left(\prod_{(i,j)\in\mu}q^{i-1}t_{j-1}\right)^{d_\mu}.$$

This is presented as a conjectural property of the multi-$t$ Macdonald polynomials and is also observed for certain normalized Yang–Baxter traces; no resolution is given.