The bounded spherical functions the free two-step nilpotent Lie group

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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 languageEnglish
Pages (from-to)351-370
Number of pages20
JournalJournal of Lie Theory
Volume16
Issue number2
Publication statusPublished - 3 Feb 2006

Keywords

  • Gelfand pair
  • Nilpotent Lie group
  • Representation theory
  • Spherical function

ASJC Scopus subject areas

  • Algebra and Number Theory

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