Hidden Supersymmetries of Deformed Supersymmetric Mechanics

Abstract: We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is arbitrary even number. Constructed models possess the hidden supersymmetry SU$(\,{\cal N}/2\,|2)$. Degeneracies of energy levels are spanned by representations of the hidden supersymmetry group.