Fourier algebras of parabolic subgroups

• Søren Knudby ^[1]
  1. [1] University of Copenhagen-DENMARK
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 2, 2017, págs. 272-290
• Idioma: inglés
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• Resumen

  • We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for this to be the case.

    As an application, we show that when P is the minimal parabolic subgroup in one of the classical simple Lie groups of real rank one or the exceptional such group, then the Fourier algebra of P coincides with the subalgebra of the Fourier-Stieltjes algebra of P consisting of functions vanishing at infinity. In particular, the regular representation of P decomposes as a direct sum of irreducible representations although P is not compact.