  We investigate the hidden symmetries of the Kerr-Newman, of the D=5 minimal
gauged supergravity which admits a Killing-Maxwell system in the sense of
Carter and of higher dimensional spacetimes in the presence of Killing-Yano
torsion. 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 (primary conformal Killing-Yano)
tensor or a PGCKY (primary generalized conformal Killing-Yano) tensor, the
latter in the presence of torsion. We point out the structure of the Dirac-type
operators of the spinning point particle in arbitrary- dimensional spacetimes
with torsion, focusing on the case when torsion can be assimilated with a
Killing-Yano tensor and these spacetimes are endowed with towers of
Killing-Yano tensors, and hence we show the anomalies of these additional
supersymmetries cancel out in this particular case.
