C*-algebraic intertwiners for principal series: case of SL(2)

Abstract

We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL.2,$F$) for $F=\mathbb{R},\mathbb{C}$ or $\mathbb{H}$. Normalisation is achieved through the use of a Fourier transform defined on some homogenous space and twisted by a Weyl element. Normalising factors are also explicitly obtained. In the appendix we relate reducibility points to a certain distribution arising from the non-normalised intertwiners.