Non-compact Young diagrams
Dmytro VOLIN
Trinity College Dublin
Mercredi 15/03/2017, 11h00
Pièce 35, Bât. 774, Orme des Merisiers

\noindent ``Integrability meeting ENS/IPhT'' \\ \par We introduce the notion of extended Young diagram to label irreducible unitary representations of non-compact supersymmetric group SU$(n,m \mid k)$. Similarly to the case of ordinary Young diagrams, the extended diagram is essentially non-sensitive to the rank of the group and hence it serves to define representations of SU$(n,m \mid k)$ with various different n,m,k. Thus one can deduce some interesting morphisms e.g. between characters of SU$(n,m \mid k)$ and ordinary Schur polynomials. \par We will also discuss how these diagrams can be used towards finding the complete set of solutions of Bethe equations for rational integrable spin chains with SU$(n,m \mid k)$ symmetry. \\ \\ (IPhT organizer: Ivan Kostov)

Contact : Loic BERVAS

 

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