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Journal Article



Alldridge,  Alexander
Max Planck Institute for Mathematics, Max Planck Society;


Hilgert,  Joachim
Max Planck Institute for Mathematics, Max Planck Society;


Wurzbacher,  Tilmann
Max Planck Institute for Mathematics, Max Planck Society;

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Alldridge, A., Hilgert, J., & Wurzbacher, T. (2018). Superorbits. Journal of the Institute of Mathematics of Jussieu, 17(5), 1065-1120. doi:10.1017/S147474801600030X.

Cite as: https://hdl.handle.net/21.11116/0000-0004-467B-4
We study actions of Lie supergroups, in particular, the hitherto elusive notion of orbits through odd (or more general) points. Following categorical principles, we derive a conceptual framework for their treatment and therein prove general existence theorems for the isotropy (or stabiliser) supergroups and orbits through general points. In this setting, we show that the coadjoint orbits always admit a (relative) supersymplectic structure of Kirillov–Kostant–Souriau type. Applying a family version of Kirillov’s orbit method, we decompose the regular representation of an odd Abelian supergroup into an odd direct integral of characters and construct universal families of representations, parametrised by a supermanifold, for two different super variants of the Heisenberg group.