INDUCED REPRESENTATIONS AND INVARIANT INTEGRAL-OPERATORS FOR SU(2,2)

The elementary representations (ER) of SU(2, 2) induced from the three non-trivial parabolic subgroups P0, P1, P2 are explicitly constructed in two equivalent realizations. We exhibit a one-to-one correspondenc e between the P0 and P2 induced representations. The corresponding rep resentations are equivalent. We also exhibit a two-to-one corresponden ce between the P1 ERs and a subset of the P0 ERs; however, the corresp onding representations are only partially equivalent. The Knapp-Stein integral intertwining operators are explicitly given for all represent ations in consideration.