Superorbits
Abstract
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.
Cite
@article{arxiv.1502.04375,
title = {Superorbits},
author = {Alexander Alldridge and Joachim Hilgert and Tilmann Wurzbacher},
journal= {arXiv preprint arXiv:1502.04375},
year = {2016}
}
Comments
47 pages; v3: final version, accepted for publication in J. Math. Inst. Jussieu