Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série SEM-DARBOUX
Domaines hep-th
Date Jeudi 28 Novembre 2024
Heure 11:00
Institut LPTHE
Salle bibliothèque du LPTHE, tour 13-14, 4eme étage
Nom de l'orateur Hernandez
Prenom de l'orateur David
Addresse email de l'orateur david [dot] hernandez [at] imj-prg [dot] fr
Institution de l'orateur IMJ-PRG
Titre Folded quantum integrable models, deformed W-algebras and representations of quantized Coulomb branches
Résumé Deformed W-algebras are two parameter algebras associated to a simple Lie algebra g, obtained from fields commuting with screening operators. We discuss some remarkable specializations of deformed W-algebras. (1) Classical limit : We propose a novel quantum integrable model for every non- simply laced simple Lie algebra g (joint work with Frenkel and Reshetikhin). 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. (2) Mixed limit : we use this limit to state a general conjecture on the parametrization of simple modules of non simply-laced shifted quantum affine algebras (closely related to quantized Coulomb branches). We have several evidences, including a general result for simple finite-dimensional representations.
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