Folded quantum integrable models and deformed W-algebras

We propose a novel quantum integrable model for every non-simply laced simple Lie algebra $${{\mathfrak {g}}}$$ , which we call the folded model. Its spectra correspond to solutions of Bethe Ansatz equations obtained by folding standard associated with affine $$U_q(\widehat{{{\mathfrak {g}}}'})$$ simply {g}}}'$$ corresponding . Our construction is motivated analysis second classical limit deformed W-algebra interpret as “folding” Grothendieck ring finite-dimensional representations conjecture, and verify in number cases, that spaces states can be identified $$U_q({}^L{\widehat{{{\mathfrak {g}}}}})$$ where $$^L{\widehat{{{\mathfrak {g}}}}}$$ (twisted) Kac–Moody Langlands dual $${\widehat{{{\mathfrak discuss analogous structures Gaudin appears $$q \rightarrow 1$$ Finally, describe conjectural -crystals terms q-characters.