Boundary three-point function on AdS2 D-branes

Using the H3+-Liouville relation, I explicitly compute the boundary three-point function on AdS2 D-branes in H3+, and check that it exhibits the expected symmetry properties and has the correct geometrical limit. I then find a simple relation between this boundary three-point function and certain fusing matrix elements, which suggests a formal correspondence between the AdS2 D-branes and discrete representations of the symmetry group. Concluding speculations deal with the fuzzy geometry of AdS2 D-branes, strings in the Minkowskian AdS3, and the hypothetical existence of new D-branes in H3+.