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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

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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