Current presentation for the super-Yangian double and Bethe vectors
Stanislav Pakuliak
Dubna, Russia
Lundi 20/02/2017, 11h00-12h00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers

We discuss the relation between RTT and current presentations for the super-Yangian double associated with the algebra $gl(m \mid n)$. This relation is used to construct the explicit formulas for the 'universal' off-shell Bethe vectors for the quantum integrable models associated with the super Yangians based on the algebras $gl(m \mid n)$. These formulas are given as the sums over partitions of the sets of the Bethe parameters and they are obtained by calculation of the certain projections from the products of the generating series of the Yangian current generators. This calculation is an effective way to resolve relations of the hierarchical Bethe ansatz and as result of this calculation we formulate simple combinatorial rules how to associate each summand in the explicit formula for the Bethe vectors with the given partition of the Bethe parameters.

Contact : Vincent PASQUIER

 

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