ABSTRACT
In this chapter we study two families of unitary representations of F r https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003071747/9455763b-cb5e-4c79-bdd6-3c0df1a0015b/content/eq889.tif"/> : the principal series and the complementary series. These series are the exact analogues of the corresponding principal and complementary series of a semislmple Lie group, say SL(2, ℝ). We show that every positive definite spherical function which is not a character determines, up to unitary equivalence, a representation of the principal or complementary series, and that these representations are irreducible and nonequivalent.
