AI 中文总结
本文研究带有相容复结构的哈密顿$H$-空间$Y$的诱导构造，提出将标准诱导中$T^*G$替换为$G$的Grauert管的伪-凯勒诱导方法，聚焦于容许整体Grauert管的李群开展研究。
AI 中文摘要
给定闭子群$H\subseteq G$与哈密顿$H$-空间$Y$，可构造诱导哈密顿$G$-空间。本文在$Y$带有相容复结构的框架下研究该构造，旨在发展该框架下的辛诱导并建立对应经典结果的凯勒类比。核心思路是将标准诱导构造$\operatorname{Ind}$中出现的余切丛$T^*G$替换为$G$的Grauert管，聚焦于容许整体定义Grauert管的李群，研究由此得到的伪-凯勒诱导程序。
英文摘要
Given a closed subgroup $H\subseteq G$ and a Hamiltonian $H$-space $Y$, one can construct an induced Hamiltonian $G$-space. In this paper we investigate this construction in the setting where $Y$ is endowed with a compatible complex structure. Our aim is to develop symplectic induction in this framework and to establish the corresponding Kähler analogues of the classical results. The main idea is to replace the cotangent bundle $T^*G$, appearing in the standard construction of $\operatorname{Ind}$, with the Grauert tube of $G$. We focus on Lie groups admitting a globally defined Grauert tube and study the resulting pseudo--Kähler induction procedure.
