Unitary representations of super Lie groups

V. S. Varadarajan
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V. S. Varadarajan: University of California, Department of Mathematics

Chapter Chapter 5 in Reflections on Quanta, Symmetries, and Supersymmetries, 2011, pp 121-153 from Springer

Abstract: 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.

Keywords: Unitary Representation; Clifford Algebra; Spin Representation; Spin Module; Semi Direct Product (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-0667-0_5

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