I will present recent progress in the understanding of two-dimensional sigma-models on the supergroup PSl(nIn). I will emphasize the relevance of these models to study quantum integrability in the AdS/CFT correspondence. In particular i will explain the computation of the fusion of some line operators, the transfer matrices, that encode an infinite number of conserved charges. This computation leads to a first-principle, perturbative derivation of the Hirota equation, which has been argued to provide a solution to the spectrum problem in N=4 SYM.