  We consider bosonic strings propagating on Euclidean adS_3, and study in
particular the realization of various worldsheet symmetries. We give a proper
definition for the Brown-Henneaux asymptotic target space symmetry, when acting
on the string action, and derive the Giveon-Kutasov-Seiberg worldsheet contour
integral representation simply by using Noether's theorem. We show that making
identifications in the target space is equivalent to the insertion of an
(exponentiated) graviton vertex operator carrying the corresponding charge.
Finally, we point out an interesting relation between 3D gravity and the
dynamics of the worldsheet on adS_3. Both theories are described by an
SL(2,C)/SU(2) WZW model, and we prove that the reduction conditions determined
on one hand by worldsheet diffeomorphism invariance, and on the other by the
Brown-Henneaux boundary conditions, are the same.
