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

2011/12/21 by Clare, Pierre
#22D25 #22E46 #46L08 #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1112.5019

Abstract

We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL(2). 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 explicitely obtained. In the appendix we relate reducibility points to a certain distribution arising from the non-normalised intertwiners.

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