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We study neutrino masses in the framework of the supersymmetric inverse seesaw model. Different from the non-supersymmetric version a minimal realization with just one pair of singlets is sufficient to explain all neutrino data. We compute the neutrino mass matrix up to 1-loop order and show how neutrino data can be described in terms of the model parameters. We then calculate rates for lepton flavour violating (LFV) processes, such as $\mu \to e \gamma$, and chargino decays to singlet scalar neutrinos. The latter decays are potentially observable at the LHC and show a characteristic decay pattern dictated by the same parameters which generate the observed large neutrino angles.

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