Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth,math,math.MP 
Date  Jeudi 18 Janvier 2018 
Heure  11:00 
Institut  LPTHE 
Salle  bibliothèque 
Nom de l'orateur  Hernandez 
Prenom de l'orateur  David 
Addresse email de l'orateur  david [dot] hernandez [at] imjprg [dot] fr 
Institution de l'orateur  IMJPRG 
Titre  Spectra of quantum integrable systems, Langlands duality and category O 
Résumé  The spectrum of a quantum integrable system is crucial to understand its properties. Rmatrices give powerful tools to study such spectra. A better understanding of transfermatrices obtained from Rmatrices led to the proof of several results for the corresponding quantum integrable systems. In particular, their spectra can be described in terms of "Baxter polynomials". They appear naturally in the study of a category O of representation of a Borel subalgebra of a quantum affine algebra. Remarkable relations in the Grothendieck ring of this category O can be established, from which one can derive the Bethe Ansatz equations between the roots of the Baxter polynomials. Based on joint works with M. Jimbo, E. Frenkel and B. Leclerc. 
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