  We investigate torsional Alfv\'{e}n modes of relativistic stars with a global
dipole magnetic field. It has been noted recently (Glampedakis et al. 2006)
that such oscillation modes could serve as as an alternative explanation (in
contrast to torsional crustal modes) for the SGR phenomenon, if the magnetic
field is not confined to the crust. We compute global Alfv\'{e}n modes for a
representative sample of equations of state and magnetar masses, in the ideal
MHD approximation and ignoring $\ell \pm 2$ terms in the eigenfunction. We find
that the presence of a realistic crust has a negligible effect on Alfv\'{e}n
modes for $B > 4\times 10^{15}$ G. Furthermore, we find strong avoided
crossings between torsional Alfv\'{e}n modes and torsional crust modes. For
magnetar-like magnetic field strengths, the spacing between consecutive
Alfv\'{e}n modes is of the same order as the gap of avoided crossings. As a
result, it is not possible to identify modes of predominantly crustal character
and all oscillations are predominantly Alfv\'{e}n-like. Interestingly, we find
excellent agreement between our computed frequencies and observed frequencies
in two SGRs, for a maximum magnetic field strenght in the range of
(0.8--1.2)$\times 10^{16}$ G.

Astrophysics;General Relativity and Quantum Cosmology