论文标题
部分可观测时空混沌系统的无模型预测
On the asymptotic support of Plancherel measures for homogeneous spaces
论文作者
论文摘要
令$ g $为真正的线性还原组，让$ h $成为一个纯模型的本地代数亚组。令$ \ operatorname {spep} l^2（g/h）$为$ g $的不可约统一表示，贡献了$ l^2（g/h）$的分解，即对plancherel措施的支持。在本文中，我们将将$ \ operatotorName {spup} l^2（g/h）$与矩形束的矩映射图像相关联$ t bundle $ t^*（g/h）\与\ mathfrak {g}^*$。对于同质空间$ x = g/h $，我们附加了$ g $的复杂化的复杂Levi子组$ l_x $，我们在某种意义上表明，在$ \ operatotorname {supp} l^2（g/h）$中，“大多数”表示是作为量化的coadechaint Orbits $ \ albits $ \ nime plance of coadearkoint Orbits un g/l $，$ l $的复杂化与$ l_x $共轭。此外，此类coadexhight Orbits $ \ Mathcal {o} $的结合与MONTS MAP图像渐近地重合。作为推论，我们表明$ l^2（g/h）$具有离散的系列，如果MONM MAP图像包含椭圆元素的非空子集。
Let $G$ be a real linear reductive group and let $H$ be a unimodular, locally algebraic subgroup. Let $\operatorname{supp} L^2(G/H)$ be the set of irreducible unitary representations of $G$ contributing to the decomposition of $L^2(G/H)$, namely the support of the Plancherel measure. In this paper, we will relate $\operatorname{supp} L^2(G/H)$ with the image of moment map from the cotangent bundle $T^*(G/H)\to \mathfrak{g}^*$. For the homogeneous space $X=G/H$, we attach a complex Levi subgroup $L_X$ of the complexification of $G$ and we show that in some sense "most" of representations in $\operatorname{supp} L^2(G/H)$ are obtained as quantizations of coadjoint orbits $\mathcal{O}$ such that $\mathcal{O}\simeq G/L$ and that the complexification of $L$ is conjugate to $L_X$. Moreover, the union of such coadjoint orbits $\mathcal{O}$ coincides asymptotically with the moment map image. As a corollary, we show that $L^2(G/H)$ has a discrete series if the moment map image contains a nonempty subset of elliptic elements.
