11 problems

Let $B^{r,s}$ be a crystal of type $D_n^{(1)}$. Let $B(\Lambda)$ denote the classical $D_n$-crystal of highest weight $\Lambda$, and let the complement of a partition $\Lambda$ in…

Type D affine crystal conjecture. If $B^{r,s}$ exists, then

Let ${\mathfrak g}$ be a simple Lie algebra with Cartan matrix $C$, let ${\mathbf R}=\{a_p\omega_{i_p}:1\leq p\leq N\}$ be a collection of dominant integral weights, and let…

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 b…

Kirillov–Reshetikhin crystal-base conjecture. For some $\zeta^{(i)}_s\in\mathbb{C}(q)^\times$, the module $W^{(i)}_s(\zeta^{(i)}_s)$ has a crystal base $\mathcal{B}^{i,s}$ that is…

Right-splitting morphism conjecture. The stated right-splitting morphism and its extension after tensoring with any such $B$ exist with the asserted injectivity and preservation of…

Transfer-matrix q-character conjecture. The identification

Kirillov–Reshetikhin K-matrix conjecture. Symmetrizable invertible solutions of the generalized spectral reflection equation in tensor products of Kirillov–Reshetikhin modules, wit…

Let $I$ be the set of Dynkin labels, let $I_<\subset I$ be the labels of the short roots in types $B_N$ and $C_N$, and let $t_a=2$ for $a\in I_<$ and $t_a=1$ otherwise. Let…

Let $\mathfrak g$ be a Lie algebra and let $\mathcal H=\bigotimes_{j=1}^N V_j$ be a tensor product of Kirillov–Reshetikhin modules. Write … and let $M_{\lambda,\mathbf n}$ be the n…

Let $\mathfrak{g}$ be a simple Lie algebra. For dominant integral $\lambda$ and multiplicity data $\mathbf n$, let $M_{\lambda,\mathbf n}^{(k)}$ and $N_{\lambda,\mathbf n}^{(k)}$ b…