# nLab super multiplet

### Context

#### Representation theory

representation theory

geometric representation theory

supersymmetry

# Contents

## Idea

A supermultiplet is an irreducible representation of a supersymmetry supergroup or super Lie algebra, decomposed as a direct sum (branching) of irreps of the underlying ordinary group.

For the case of unitary representations of the super Poincaré group, then under the canonical inclusion of the ordinary Poincaré group into the super Poincaré group, the supermultiplets for super-isometries of super Minkowski spacetime decompose into a direct sum of irreducible unitary representations of the Poincaré group. Via the Wigner classification of fundamental particles as irreps of the Poincaré group, this gives a decomposition of supermultiplets into particle species. The particles in this direct sum related by odd supersymmetry transformations are called superpartners.

Similar statements hold for the super anti de Sitter group or superconformal group etc.

By Deligne's theorem on tensor categories the most general regular tensor categories are those spanned by supermultiplets for some supergroup.