  We show that D-branes in the Euclidean $AdS_3$ can be naturally associated to
the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This
picture makes very transparent the residual loop group symmetry of the D-brane
configurations and gives also immediately the D-branes shapes and the
$\sigma$-model boundary conditions in the de Sitter T-dual of the
$SL(2,C)/SU(2)$ WZW model.
