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 correspondence between the P₀ and P₂ induced representations. The corresponding representations are equivalent. We also exhibit a two-to-one correspondence between the P₁ ERs and a subset of the P₀ ERs; however, the corresponding representations are only partially equivalent. The Knapp-Stein integral intertwining operators are explicitly given for all representations in consideration.