Abstract
The concept of a unitary representation(UR) of a super Lie group is formulated via super Harish-Chandra pairs. For super semidirectproducts the classical Wigner-Mackey theory of little groups works perfectly in the supersymmetric setting, and leads to a description of all of their unitary irreducible representations (UIR). The Clifford structure of the representations and the concept of super multiplets all make sense in the general context of super semidirect products, which includes all cases studied by the physicists, and leads to many of their major predictions: multiplet structure (both for minimal and extended supersymmetry), and the famous susy partners.
This essay is partly based on the lectures I gave at a conference on supersymmetry held in Oporto, Portugal, in 2006. I am grateful to the organizers of that conference for their splendid hospitality. I also wish to thank Claudio Carmeli, Gianni Cassinelli, Dan Freed, Marian Lledo, and Albert Schwarz for several stimulating conversations during the conference. See also [1a, 1b].
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Varadarajan, V.S. (2011). Unitary representations of super Lie groups. In: Reflections on Quanta, Symmetries, and Supersymmetries. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0667-0_5
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