Status  Confirmed 
Seminar Series  SEMDARBOUX 
Subjects  hepth,math,math.MP 
Date  Thursday 18 January 2018 
Time  11:00 
Institute  LPTHE 
Seminar Room  bibliothèque 
Speaker's Last Name  Hernandez 
Speaker's First Name  David 
Speaker's Email Address  david [dot] hernandez [at] imjprg [dot] fr 
Speaker's Institution  IMJPRG 
Title  Spectra of quantum integrable systems, Langlands duality and category O 
Abstract  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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