Journal of Noncommutative Geometry

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Volume 9, Issue 1, 2015, pp. 1–19
DOI: 10.4171/JNCG/185

Published online: 2015-04-13

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

Pierre Clare[1]

(1) Dartmouth College, Hanover, USA

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.

Keywords: Group C-algebras, Hilbert modules, semisimple Lie groups, principal series representations, intertwining operators

Clare Pierre: C*-algebraic intertwiners for principal series: case of SL(2). J. Noncommut. Geom. 9 (2015), 1-19. doi: 10.4171/JNCG/185