Folded quantum integrable models and deformed W-algebras

Apparaît dans les collections : 2024 - T1 - Quantum many-body systems out-of-equilibrium, ECM 2024 Invited Speakers

We propose a novel quantum integrable model for every non-simply laced simple Lie algebra g. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the Bethe Ansatz equations associated to the simply-laced Lie algebra g′ (corresponding to g). Our construction is motivated by the analysis of the second classical limit of the deformed W-algebra of g. We conjecture, and verify in a number of cases, that the spaces of states of the folded integrable model can be identified with finite-dimensional representations of the Langlands dual (twisted) quantum affine algebra.

Joint work with E. Frenkel and N. Reshetikhin.