Conjecture on the signs in the leading-matrix realization

Fix a partition $d706\vdash n+1$ and the associated quantities $d716_i$ appearing in Theorem~, with $1\leq i\leq N_{d706}$. The signs $d716_i$ are the coefficients occurring in that theorem's description of the full algebra.

Sign conjecture. In Theorem~, one has

$$\epsilon_i=1$$

for all $1\leq i\leq N_{d706}$.

This asserts that no sign changes are needed in the full matrix realization. The source does not provide a resolution, so the conjecture remains open.