3 problems

Let $b\in P_+$ correspond to a Young diagram $\mu_b$ with rows of lengths $m_i$, and let $b_i=m_i\omega_1$. Write $\operatorname{ord}$ for the order of $\mu_b$. Evaluation conjectu…

Let $b\in P_+$ correspond to a Young diagram $\mu_b$, and let $b^{tr}$ be the dominant weight corresponding to its transpose. Assume the $a=0$ specialization $H\!D_{r,s}(b;q,t,0)$…

In type $A_n$, regard a dominant weight $b\in P_+$ as a weight for every $A_m$ with $m\ge n$. Let $H\!D_{r,s}(b;q,t,a)$ denote a polynomial in non-negative integral powers of $a,q$…