3 problems

Let $\lambda$ be an arbitrary weight and let $\Gamma$ be a reduced chain of roots corresponding to $\lambda$. Write $\mathcal{A}(\Gamma)$ for the associated quantum alcove model, a…

Let $\mathcal{A}(w,\Gamma)$ be the set of admissible subsets associated with a Weyl-group element $w$ and a reduced $\lambda$-chain $\Gamma$, and suppose the identities in Theorems…

Let $\Gamma$ and $\Gamma'$ be $\lambda$-chains, and let $\mathcal{A}(\Gamma)$ and $\mathcal{A}(\Gamma')$ be the corresponding quantum alcove models. Let $B^{\otimes \mathbf{p}}$ be…