The simple finite Lie superalgebras D(2, 1;α), G(3),. D(4,1), D(2,2), A(3,1) and F(4) admit D-module representations, given by a set of differential operators of a single variable t ∈ R, at a critical value of the scaling dimension λ. These superalgebras are one-dimensional N-extended superconformal algebras with N = 4 (D(2,1; α)), N = 7 (G(3)) and N = 8 (the remaining ones). The critical D-module reps induce invariant actions in the Lagrangian framework for superconformal mechanics in D target dimensions. The N = 8 critical scalings λ = 1/(D-4) linked to the D-dimensional harmonic functions with D = 1,2,3,5,6,7,8. This talk is based on J. Math. Phys. 53 (2012) 043513 (arXiv: 1112.0995), J. Math. Phys. 53 (2012) 103518 (arXiv: 1208.3612) and some extra material.
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