Journal of Lie Theory 16 (2006), No. 2, 351--370
Copyright Heldermann Verlag 2006
The Bounded Spherical Functions on the Free Two-Step Nilpotent Lie Group
Véronique Fischer
Dept. of Mathematics, Göteborg University, 41296 Göteborg, Sweden
veronique.fischer@math.u-psud.fr
We give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the actions of orthogonal groups or their special subgroups. Next we deduce some results about the (Kohn) sub-Laplacian, and we compute the radial Plancherel measure.
Keywords: Nilpotent Lie group, representation theory, spherical function, Gelfand pair.
MSC: 22E30, 22E25, 22E27
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