超对称背景下的旗域
On Flag Domains in the Supersymmetric Setting
摘要：
旗域是复约化李群$G$的实形式$G_\mathbb{R}$在$G$ -旗超流形$Z = G/P$中的开轨道.本文从标志域理论出发，探讨了三个问题：1.可测性（即存在$G_\mathbb{R}$不变的Berezinian密度）2.全局全纯超函数3.循环空间和双纤维化变换在第二章中对相应的经典结果作了修正。本文给出了所有可测旗域的分类以及旗域上的整体全纯函数的分类。此外，最后一章提供了实约化（超）李群的表示论与复李超代数的Bott-Borel-Weyl理论之间的一个可能的联系。
英文摘要：
Flag domains are open orbits of real forms $G_\mathbb{R}$ of complex reductive Lie supergroups $G$ in $G$-flag supermanifolds $Z = G/P$. This thesis discusses three topics from the theory of these flag domains: 1. Measurability(i.e. existence of $G_\mathbb{R}$-invariant Berezinian densities) 2. Global holomorphic superfunctions 3. Cycle spaces and the Double Fibration Transform A revision of the respective classical results is included in the second chapter. This thesis provides a classification of all measurable flag domains and of the global holomorphic functions on all flag domains. Moreover, the last chapter provides a possible link between the representation theory of real reductive (super) Lie groups and the Bott-Borel-Weyl Theory for complex Lie superalgebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
