Elementary representations and intertwining operators for the group SU1(4)

Global realizations of all elementary induced representations (EIR) of the group SU¹(4), which is the double covering group of SO↑(5,1), are given. The Knapp-Stein intertwining operators are constructed and their harmonic analysis carried out. The invariant subspaces of the reducible EIR are introduced and the differential intertwining operators between partially equivalent EIR are defined. Invariant sequilinear forms on pairs of invariant subspaces are constructed. Differential identities between invariant sesquilinear forms on pairs of irreducible components of the reducible representations are derived. The results will be applied elsewhere to the nonpertubative analysis of Euclidean conformal invariant quantum field theory with fields of arbitrary spin.