Supergroup Actions and Harmonic Analysis

What is it about?

Kirillov’s orbit philosophy holds for nilpotent Lie supergroups in a narrow sense, but due to the paucity of unitary representations, it falls short of being an effective tool of harmonic analysis in its present form. In this note, we survey an approach using families of coadjoint orbits which remedies this deficiency, at least in relevant examples.

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