Fourier algebras of parabolic subgroups
Keyword(s):
Rank One
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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.
1985 ◽
Vol 37
(4)
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pp. 635-643
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2005 ◽
Vol 04
(06)
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pp. 683-706
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Keyword(s):
2019 ◽
Vol 31
(08)
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pp. 1950026
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2017 ◽
Vol 28
(10)
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pp. 1750067
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Keyword(s):