论文标题
一层双曲线上的线条束的显式倾斜公式
An explicit Plancherel formula for line bundles over the one-sheeted hyperboloid
论文作者
论文摘要
在本文中，我们考虑$ g = \ operatatorName {sl}（2，\ mathbb {r}）$和$ h $是对角矩阵的子组。然后$ x = g/h $是一个单型均匀的空间，可以用一片曲折的倍曲底识别。对于$ h $的每个单一字符$χ$，我们将诱导的表示形式分解为不可约合的单一表示形式，称为plancherel公式。这是通过研究$ \ operatatorName {ind} _h^g（χ）$和$ g $的主序列表示形式之间的明确交织操作员来完成的。这些运算符取决于感应参数。
In this paper we consider $G=\operatorname{SL}(2,\mathbb{R})$ and $H$ the subgroup of diagonal matrices. Then $X=G/H$ is a unimodular homogeneous space which can be identified with the one-sheeted hyperboloid. For each unitary character $χ$ of $H$ we decompose the induced representations $\operatorname{Ind}_H^G(χ)$ into irreducible unitary representations, known as a Plancherel formula. This is done by studying explicit intertwining operators between $\operatorname{Ind}_H^G(χ)$ and principal series representations of $G$. These operators depends holomorphically on the induction parameters.
