Invariant generalized functions on sl(2,R) with values in a sl(2,R)-module

To solve this problem we find all the locally invariant generalized functions supported in the nilpotent cone N. We do this locally in a neighborhood of a nilpotent element Z of g (cf. Theorem 4.1) and on an SL(2,R)-invariant open subset U⊂sl(2,R) (cf. Theorem 4.2). Finally, we also give an application of our main theorem to the Superpfaffian (Superpfaffian, prepublication, e-print math.GR/0402067, 2004).