This talk is based on joint work with Andrei Negut (arXiv: 2606.02471). We recall Kac–Moody algebras of twisted affine type, emphasizing the difficulties that arise in the quantum group setting. We state David Hernandez’s conjecture relating the representation theories of quantum affine algebras of untwisted and twisted types. We then explain the tools we use to prove this conjecture and extend it to much more general settings: the shuffle algebra interpretation of quantum loop algebras and Negut’s q-character formula for representations of shuffle algebras.
