4 problems

Parabolic positivity conjecture. If $\bar{\mu^*}$ is a partition, then $K_{\lambda;\mu^*}(q)$ has non-negative integer coefficients. These polynomials are introduced as $q$-analogs…

Let $R=\{(r_i,s_i)_{i=1}^L\}$ be a sequence of rectangles, and let $\mathcal{P}_R$ be the set of paths in the tensor product … For a path $p$, let $\operatorname{wt}(p)$ be its wei…

Parabolic Kostka duality conjecture. There is a constant $C$ such that

Let $R=\{(r_i,s_i)_{i=1}^L\}$ be a sequence of rectangles, and let $\mathcal{P}_R$ be the set of all paths, including non-highest elements, in the tensor product … For a path $p$,…