3 problems

Let $n$ and $l$ be positive integers, and let $X^{(l)}{ u}(\rho)$, $X^{(l)'}{ u}(\rho)$, $F^{(l)}{ u}(q)$, and $F^{(l)'}{ u}(q)$ denote the restricted one-dimensional sums and fermio…

Let $G$ be one of the classical groups and let $\mu^{(1)},...,\mu^{(r)}$ and $\lambda$ index the corresponding $q$-analogue $\frak{D}_{\mu^{(1)},...,\mu^{(r)}}^{\lambda,G}(q)$ of a…

Schilling–Shimozono conjecture. For $\diamondsuit\in\{(1),(2),(1,1)\}$,