On Flag Domains in the Supersymmetric Setting

Flag domains are open orbits of real forms $G_{\mathbb{R}}$ of complex reductive Lie supergroups $G$ in $G$-flag supermanifolds $Z=G\mathrm{/}P$. 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.