TY - JOUR
AU - Knudby, SÃ¸ren
PY - 2017/05/27
Y2 - 2022/01/22
TI - Fourier algebras of parabolic subgroups
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 120
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-25624
UR - https://www.mscand.dk/article/view/25624
SP - 272-290
AB - <p>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.</p><p>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.</p>
ER -