On Drinfeld’s second realization of the AdS/CFT su(2|2)su(2|2) Yangian

We construct Drinfeld’s second realization of the Yangian based on psu(2|2)⋉R3psu(2|2)⋉R3 symmetry. The second realization is traditionally more suitable for deriving the quantum double and the universal RR-matrix with respect to the first realization, originally obtained by Beisert, and it is generically more useful in order to study finite-dimensional representations. We show that the two realizations are isomorphic, where the isomorphism is almost the standard one given by Drinfeld for simple Lie algebras, but needs some crucial corrections to account for the central charges. We also evaluate the generators of the second realization on the fundamental representation, finding the interesting result that the rapidity variable for some generators gets boosted by the energy eigenvalue.