10 problems

Folding conjecture. The $q$-characters of the simple modules $L(\boldsymbol{\psi})$ of $U_q(L{\mathfrak{g}})$ and $L(\rho(\boldsymbol{\psi}))$ of $U_q(L{\mathfrak{g}}^\sigma)$ sati…

Let $\mathfrak{g}$ be a simply laced simple Lie algebra and let $\tau$ be a diagram automorphism. Let $\mathfrak{g}_\tau$ be the non-simply laced Lie algebra Langlands dual to the…

Let $G=ADE$ and let $G'$ be a folding of $G$. Write $\mathrm{CFT}(A_1,G)$ and $\mathrm{CFT}(A_1,G')$ for the two-dimensional conformal field theories associated with these Dynkin d…

Let $\phi_n$ be the homomorphism folding $q$-characters of integrable $\mathcal{U}_q({\widehat{\mathfrak{sl}_{\infty}}})$-modules to virtual $q$-characters of integrable…

Let $\mathfrak g$ be simply laced, let $\sigma$ be the folding data, and let $\phi^\sigma_{\mathfrak g}$ and $\Phi^\sigma_{\mathfrak g}$ be the monomial and Grothendieck-ring foldi…

Consider the folding homomorphism from the Grothendieck ring of finite-dimensional representations of an untwisted quantum loop algebra to that of the corresponding twisted quantum…

A polyomino is a connected union of unit squares in the square lattice, with cuts between squares permitted; it is cube-foldable if it can be folded along its edges to cover the su…

Let $\mathfrak{g}$ be of type $A_{2n-1}$, let $\bar\pi$ be the induced homomorphism from the Grothendieck ring of finite-dimensional representations of the non-twisted quantum affi…

Folding conjecture. All extended $u$-equations in multiply-laced type come from folding.

Let $\mathfrak{g}$ be a Lie algebra, let $\sigma$ be an admissible diagram automorphism, and let $\mathfrak{g}_+$, $\mathfrak{n}$, $R(w_\circ)$, $\iota_\mathbf{i}$, and…