$$Q{\widetilde{Q}}$$-Systems for Twisted Quantum Affine Algebras

Abstract

We establish the \(Q {\widetilde{Q}}\)-systems for the twisted quantum affine algebras that were conjectured in Frenkel and Hernandez (Commun Math Phys 362(2):361–414, 2018). We develop the representation theory of Borel subalgebra of twisted quantum affine algebras and we construct their prefundamental representations. We also propose a general conjecture on the relations between twisted and non-twisted types. We prove this conjecture for some particular classes of representations, including prefundamental representations.