Fourier algebras of parabolic subgroups
Fourier algebras of parabolic subgroups
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抛物线子群的傅立叶代数
DOI：
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发表时间：
2013
期刊：
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通讯作者：
Søren Knudby
中科院分区：
文献类型：
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作者：
Søren Knudby
我们研究以下问题：给定一个局部紧群，当它的傅里叶代数与由无穷远为零的函数组成的傅里叶-斯蒂尔吉斯代数的子代数重合时？我们为这种情况提供了充分的条件。
作为应用，我们证明了当P是真实的秩为1的经典单李群或例外单李群中的极小抛物子群时，P的Fourier代数与P的由无穷远为零的函数组成的Fourier-Stieltjes代数的子代数重合.特别地，P的正则表示分解为不可约表示的直和，尽管P不是紧的。
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.