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We computed the actions for the 1D N=5 sigma-models with respect to the twoinequivalent (2,8,6) multiplets. 4 supersymmetry generators are manifest, whilethe constraint originated by imposing the 5-th supersymmetry automaticallyinduces a full N=8 off-shell invariance. The resulting action coincides in thetwo cases and corresponds to a conformally flat 2D target satisfying a specialgeometry of rigid type. To obtain these results we developed a computationalmethod (for Maple 11) which does not require the notion of superfields and isinstead based on the nowadays available list of the inequivalentrepresentations of the 1D N-extended supersymmetry. Its application tosystematically analyze the sigma-models off-shell invariant actions for theremaining N=5,6,7,8 (k,8,8-k) multiplets, as well as for the N>8representations,only requires more cumbersome computations.

One-dimensional sigma-models with N=5,6,7,8 off-shell supersymmetries