On hidden broken nonlinear superconformal symmetry of conformal   mechanics and nature of double nonlinear superconformal symmetry
  We show that for positive integer values $l$ of the parameter in the conformal mechanics model the system possesses a hidden nonlinear superconformal symmetry, in which reflection plays a role of the grading operator. In addition to the even $so(1,2)\oplus u(1)$-generators, the superalgebra includes $2l+1$ odd integrals, which form the pair of spin-$(l+{1/2})$ representations of the bosonic subalgebra and anticommute for order $2l+1$ polynomials of the even generators. This hidden symmetry, however, is broken at the level of the states in such a way that the action of the odd generators violates the boundary condition at the origin. In the earlier observed double nonlinear superconformal symmetry, arising in the superconformal mechanics for certain values of the boson-fermion coupling constant, the higher order symmetry is of the same, broken nature. 
Francisco Correa, Mariano A. del Olmo and Mikhail S. Plyushchay