Abstract
In this paper, 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.
Original language | English |
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Pages (from-to) | 351-370 |
Number of pages | 20 |
Journal | Journal of Lie Theory |
Volume | 16 |
Issue number | 2 |
Publication status | Published - 3 Feb 2006 |
Keywords
- Gelfand pair
- Nilpotent Lie group
- Representation theory
- Spherical function
ASJC Scopus subject areas
- Algebra and Number Theory