Journal of Lie Theory

no. 2
The Bounded Spherical Functions on the Free Two-Step Nilpotent Lie Group
Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 351-370
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.
DOI: 10.5802/jolt.414
Classification: 22E30, 22E25, 22E27
Keywords: Nilpotent Lie group, representation theory, spherical function, Gelfand pair 
@article{JOLT_2006_16_2_a8,
     author = {V. Fischer},
     title = {The {Bounded} {Spherical} {Functions} on the {Free} {Two-Step} {Nilpotent} {Lie} {Group}},
     journal = {Journal of Lie Theory},
     pages = {351--370},
     year = {2006},
     volume = {16},
     number = {2},
     doi = {10.5802/jolt.414},
     zbl = {1101.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.414/}
}
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V. Fischer. The Bounded Spherical Functions on the Free Two-Step Nilpotent Lie Group. Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 351-370. doi: 10.5802/jolt.414

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