4 problems

Let $K=K_{r,s}$ be a knot with $r,s\in\mathbf{Z}$, and let $b$ be a dominant weight for all $B_m$ with $m\ge n\ge2$. Type-B hyper-polynomial conjecture. There exists a polynomial…

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-…

Let $K=K_{r,s}$ be a knot with $r,s\in\mathbf{Z}$, and let $b=\sum_{i=1}^{n}c_i\epsilon_i$ be dominant for all $C_m$ with $m\ge n\ge2$. Type-C hyper-polynomial conjecture. There ex…

Let $\mathcal{H}^{C}_{r,s}(b;q,t,u,a)$ denote the type-$C$ hyper-polynomial and let $\widetilde{J\!D}^{C_m}_{r,s}$ be the corresponding type-$C_m$ DAHA-Jones polynomial. Existence…