Super Quantization
Let G be a compact connected real semisimple Lie group. According to Gelfand, a model of G is a unitary G-representation in which every equivalence class of irreducible representation occurs once. Using the method of geometric quantization it is possible to construct such a model: the representations occur in the space of holomorphic sections of line bundles on X an homogeneous space for G. When G is not compact the situation is more complicated and the notion of model has to be accordingly modified. We want to extend this theory to the super setting: we realize unitary representations of connected real semisimple super groups (not necessarily compact) in the space of holomorphic sections of super line bundles on K¨ahler supermanifolds.