hidden symmetries and killing spinor of 5-dimensional minimal gauged supergravity solutions

We investigate the hidden symmetries and existence of killing spinors of d=5 minimal gauged supergravity solutions which admit a killing-maxwell system in the sense of carter, such as the chong-cvetic-lü-pope (cclp) kerr-ds black hole spacetime and a 5-dimensional minimal gauged supergravity solution endowed with a sasaki structure deformed by torsion, a limiting case of the generalization of the 5-dimensional toric sasaki-einstein la,b,c spacetime. we note that when an electromagnetic tensor is present and an associated killing-maxwell system can be constructed in the sense of carter, the killing-maxwell field becomes a pcky (principal conformal killing-yano) tensor or a pgcky (principal generalized conformal killing-yano) tensor, the latter in the presence of torsion. we find some new hidden symmetries of the chong-cvetic-lü-pope black hole, i.e. we construct two more generalized stäckel-killing tensors and the associated generalized killing-yano (gky) tensors. we also explicitly construct a killing spinor for the specific 5-dimensional minimal gauged supergravity solution that is endowed with a sasaki structure deformed by torsion mentioned above.