Fourier algebras of parabolic subgroups

  • Søren Knudby

Abstract

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.

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Published
2017-05-27
How to Cite
Knudby, S. (2017). Fourier algebras of parabolic subgroups. MATHEMATICA SCANDINAVICA, 120(2), 272-290. https://doi.org/10.7146/math.scand.a-25624
Section
Articles