Supersymmetric oscillator: Novel symmetries

We discuss various continuous and discrete symmetries of the supersymmetric simple harmonic oscillator (SHO) in one (0+1)-dimension of spacetime and show their relevance in the context of mathematics of differential geometry. We show the existence of a novel set of discrete symmetries in the theory which has, hitherto, not been discussed in the literature on theoretical aspects of SHO. We also point out the physical relevance of our present investigation. Copyright (C) EPLA, 2012