AI 中文总结
本文证明了在约化李群对$(G,H)$中，当$G$满足线性等假设时，离散可分解性的相伴簇条件对任意约化子群$H$也是充分的，并给出其与$\mathfrak{h}$-可容许性等价的推论。
AI 中文摘要
本文研究约化李群$G$的不可约表示限制到约化子群$H$时何时是离散可分解的。T. Kobayashi给出了离散可分解性在相伴簇意义上的一个必要条件。在之前的一篇文章中，我们证明了当$(G,H)$是对称对时该条件也是充分的。本文的目的是在$G$满足某些假设（例如$G$是线性的）下，对任意约化子群$H$证明该充分性。作为应用，我们证明当$\mathfrak{h}$的紧致因子在某种意义下是极大时，离散可分解性等价于$\mathfrak{h}$-可容许性。
英文摘要
In this paper, we study when the restriction of an irreducible representation of a reductive Lie group $G$ to a reductive subgroup $H$ is discretely decomposable. T.\ Kobayashi gave a necessary condition for discrete decomposability in terms of associated varieties. In a previous paper, we proved that the condition is also sufficient if $(G, H)$ is a symmetric pair. The purpose of this paper is to prove the sufficiency for any reductive subgroup $H$ under some hypothesis on $G$ (e.g., $G$ is linear). As an application, we show that discrete decomposability is equivalent to $\mathfrak{h}$-admissibility when the compact factor of $\mathfrak{h}$ is maximal in some sense.
Comments61 pages
