9 problems

Let $\mathcal{P}$ denote the set of partitions, let $\mu\in\mathcal{P}$ and $\nu\in\mathbb{Z}^n$ satisfy $l(\mu)\leq n$ and $|\mu|=|\nu|$, and let $K_{\mu\nu}$ be the corresponding…

Generalized Q-Kostka positivity conjecture. If $\bar{\mu^*}$ is a partition, then $L_{\lambda;\mu^*}(q)$ is a polynomial in $q$ with non-negative integer coefficients. These coeffi…

Let $\lambda$ and $\mu$ be partitions, let $r$ be an integer that is not a part of either partition, and let $L_{\lambda\mu}(q)$ denote the $Q$-Kostka polynomial. Growth conjecture…

Let $L_{\lambda\mu}(q)$ denote the $Q$-Kostka polynomial, with $\lambda$ and $\mu$ partitions in the indexing convention of the paper. Positivity conjecture. The $Q$-Kostka polynom…

For partitions $\boldsymbol{\mu}$ and $\lambda$, let $c_{\boldsymbol{\mu}}^{\lambda}(q,t)$ denote the structure coefficients introduced through the product of modified Hall–Littlew…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra, with root system $\Phi$, positive roots $\Phi_+$, simple roots $\alpha_1,\ldots,\alpha_r$, and corresponding fundamental wei…

Kostka-positivity conjecture. Every $K_{\Omega\Lambda}(q,t)$ is a polynomial in $q$ and $t$ with nonnegative integer coefficients. The paper proves this conjecture in the stable se…

Concatenation conjecture. One has

Conjugation conjecture. The map $\psi$ satisfies