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arXiv · 1507.04042

On Flag Domains in the Supersymmetric Setting

Christopher Graw
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Abstract

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.

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Christopher Graw. 2015-07-14. On Flag Domains in the Supersymmetric Setting. https://arxiv.org/abs/1507.04042

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