Hybrid NLIE for the mirror AdS5 ×S5

We revisit the derivation of hybrid nonlinear integral equations of the XXX model starting from the linearization of the T-system related to spinon variables. We obtain two sets of equations, corresponding to two linearly independent solutions of the A1 TQ-relation. Recalling that the TQ-relations in the horizontal strips of the -hook is of A1 type, we replace the corresponding Y-functions by a finite number of auxiliary variables