We construct the Killing(-Yano) tensors for a large class of charged black
holes in higher dimensions and study general properties of such tensors, in
particular, their behavior under string dualities. Killing(-Yano) tensors
encode the symmetries beyond isometries, which lead to insights into dynamics
of particles and fields on a given geometry by providing a set of conserved
quantities. By analyzing the eigenvalues of the Killing tensor, we provide a
prescription for constructing several conserved quantities starting from a
single object, and we demonstrate that Killing tensors in higher dimensions are
always associated with ellipsoidal coordinates. We also determine the
transformations of the Killing(-Yano) tensors under string dualities, and find
the unique modification of the Killing-Yano equation consistent with these
symmetries. These results are used to construct the explicit form of the
Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of
dimensions and for its charged version.Comment: 87 pages. V2: typos are corrected, appendix C and references are
added. V3: several typos are fixe