Norm of Bethe vectors in $gl(m|n)$ based models

International audienceWe study quantum integrable models solvable by the nested algebraic Betheansatz and possessing $\mathfrak{gl}(m|n)$-invariant $R$-matrix. We compute thenorm of the Hamiltonian eigenstates. Using the notion of a generalized model weshow that the square of the norm obeys a number of properties that uniquely fixit. We also show that a Jacobian of the system of Bethe equations obeys thesame properties. In this way we prove a generalized Gaudin hypothesis for thenorm of the Hamiltonian eigenstates