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A super-unitary representation of the super Poincaré group (supersymmetry)
The analog in superalgebra/supergeometry of a unitary representation of the Poincaré group.
An irreducible representation of the super Poincaré Lie algebra is called a super multiplet. This is in general itself a super vector space which contains an ordinary irreducible unitary representation of the Poincaré group. Via the Wigner classification of fundamental particles with Poincaré irreps, this may be identified with a bosonic relativistic particle of some mass – together with the images of these “bosonic” elements under the odd generators: the superpartners of the bosonic particles.
Reviews and lecture notes include
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, section II.4.1 in Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
Veeravalli Varadarajan, Unitary representations of super Lie groups (pdf)
Daniel Freed, lecture 6 of Classical field theory and Supersymmetry, IAS/Park City Mathematics Series Volume 11 (2001) (pdf)
Daniel Freed, Lecture 3 of Five lectures on supersymmetry
Antoine Van Proeyen, Tools for supersymmetry (arXiv:hep-th/9910030)
The classification is due to
The analogous discussion generalized to parasupersymmetry? is in
Expositional slides: