Induced representations from the Heisenberg parabolic subgroup of SL(n+2,R)

The group G = SL(n+2,) has a parabolic subgroup $P = MAN$ whose unipotent radical is a Heisenberg group. We study representations induced from a character of P, and using the Lie algebra action on the space of K-finite vectors we find the points of reducibility and the complementary series. We identify solutions to the conformally invariant systems of differential operators as subrepresentations.