A quantum symmetry is robust against a perturbation exactly when it commutes with the limit spectral subprojections of the perturbed Hamiltonian; against all perturbations, only functions of the unperturbed Hamiltonian survive.
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Robustness of quantum symmetries against perturbations
A quantum symmetry is robust against a perturbation exactly when it commutes with the limit spectral subprojections of the perturbed Hamiltonian; against all perturbations, only functions of the unperturbed Hamiltonian survive.