  I show how the AdS2 D-branes in the Euclidean AdS3 string theory are related
to the continuous D-branes in Liouville theory. I then propose new discrete
D-branes in the Euclidean AdS3 which correspond to the discrete D-branes in
Liouville theory. These new D-branes satisfy the appropriate shift equations.
They give rise to two families of discrete D-branes in the 2d black hole, which
preserve different symmetries.
