Type-C hyper-polynomial hyper-duality conjecture

Identify dominant weights with Young diagrams and let $b^{tr}$ correspond to the transposed diagram. Let $\mathcal{H}^{C}_{r,s}(b;q,t,u,a)$ be the type-$C$ hyper-polynomial. Hyper-duality conjecture. After multiplication by a suitable monomial in $q,t,u$,

$$\mathcal{H}^{C}_{r,s}(b;q,t,u,a)=\mathcal{H}^{C}_{r,s}(b^{tr};t^{-1},q^{-1},u^{-1}t/q,-aqu).$$

This substitution is compatible with the specializations $u=-t$ and $u=-q^{-1}$. In addition, the $t=1$ evaluation factors over the rows of the Young diagram, and for $1<s<r$ the maximal power of $a$ is $\operatorname{ord}\times r$. These duality and evaluation properties are proposed for the type-$C$ hyper-polynomials and are not proved in general.