
Journal of Lie Theory 16 (2006), No. 2, 351370 Copyright Heldermann Verlag 2006 The Bounded Spherical Functions on the Free TwoStep Nilpotent Lie Group Véronique Fischer Dept. of Mathematics, Göteborg University, 41296 Göteborg, Sweden veronique.fischer@math.upsud.fr We give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free twostep nilpotent Lie groups endowed with the actions of orthogonal groups or their special subgroups. Next we deduce some results about the (Kohn) subLaplacian, and we compute the radial Plancherel measure. Keywords: Nilpotent Lie group, representation theory, spherical function, Gelfand pair. MSC: 22E30, 22E25, 22E27 [ Fulltextpdf (257 KB)] for subscribers only. 