 In the case of irreducible admissible representations of SL(2,R), it turns out that, generically, there is exactly one representation, up to an isomorphism, with the specified central and infinitesimal characters.In the exceptional cases there are two or three representations with the prescribed parameters, all of which have been determined.For each nonnegative integer "n", the group SL(2,R) has an irreducible representation of dimension "n"+1, which is unique up to an isomorphism.