The explicit Plancherel formula on the line budle of ${\rm SL}(n+1, {\mathbb R})/{\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$

Li Zhu; Liangyun Chen

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arXiv · 1607.03451

The explicit Plancherel formula on the line budle of ${\rm SL}(n+1, {\mathbb R})/{\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$

Li Zhu·Liangyun Chen

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Abstract

The purpose of this paper is to study the Plancherel formula for the spaces of $L^2$-sections of the line bundles over the pseudo-Riemannian space $G/H$, where $G={\rm SL}(n+1, {\mathbb R})$ and $H={\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$. The formula is given in an explicit form by means of spherical distributions associated with the character $\chi_{_\lambda}$ of the subgroup $H$.

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Li Zhu, Liangyun Chen. 2016-07-07. The explicit Plancherel formula on the line budle of ${\rm SL}(n+1, {\mathbb R})/{\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$. https://arxiv.org/abs/1607.03451

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