Twisted Kirillov–Reshetikhin crystal conjecture for constructed perfect crystals

Let $\widehat{\mathfrak{g}}$ be one of the twisted quantum affine algebras considered in the paper, let $\widehat{I}_0$ be its classical index set, and fix $i\in\widehat{I}_0$ and $s\in\mathbb{Z}_{\ge 1}$. Let $\widehat{\mathcal{B}}^{i,s}$ be the constructed perfect $U_q^{\prime}(\widehat{\mathfrak{g}})$-crystal, and let $\widehat{W}^{(i)}_s(\widehat{\zeta}^{(i)}_s)$ be the corresponding Kirillov–Reshetikhin module, with $\widehat{\zeta}^{(i)}_s\in\mathbb{C}(q)^\times$.

Twisted Kirillov–Reshetikhin crystal conjecture. The perfect $U_q^{\prime}(\widehat{\mathfrak{g}})$-crystal $\widehat{\mathcal{B}}^{i,s}$ is isomorphic to the conjectural crystal base of $\widehat{W}^{(i)}_s(\widehat{\zeta}^{(i)}_s)$ over $U_q^{\prime}(\widehat{\mathfrak{g}})$.

The conjecture identifies the explicitly constructed perfect crystals with the crystal bases predicted for twisted Kirillov–Reshetikhin modules. The paper gives branching rules agreeing with the conjectural rules known from the cited work, but does not establish the module-theoretic identification.