  In this paper, we consider the symmetries of the Dirac operator derived from
a connection with skew-symmetric torsion. We find that the generalized
conformal Killing-Yano tensors give rise to symmetry operators of the massless
Dirac equation, provided an explicitly given anomaly vanishes. We show that
this gives rise to symmetries of the Dirac operator in the case of strong
Kahler with torsion (KT) and strong hyper-Kahler with torsion (HKT) manifolds.
