  A brief review of string theory on group manifolds is given, and comparisons
are then drawn between Minkowski space, SU(2), and SU(1,1) = AdS_3. The proof
of the no-ghost theorem is outlined, assuming a certain restriction on the
representation content for bosonic and fermionic strings on SU(1,1). Some
possible connections with the AdS/CFT correspondence are mentioned. (Based on
invited talk by JME at Trieste Conference on Super 5-branes and Physics in
(5+1)-dimensions.)
