Matchete`
Matchete`

CRep

CRep[rep]

denotes the conjugate of a representation.

Details and Options

  • The basis of a conjugate representation is the dual basis to the representation itself. This is no the case for the DualRepresentation, although the two are isomorphic.
  • Representations are labeled with a list of integers corresponding to the Dynkin coefficients of the highest weight in the representation.

Examples

Basic Examples  (2)

As an example, the weights of the anti-fundamental representation of SU(3) are different depending on whether we specify the representation as CRep[{1, 0}] or as {0, 1}:

The weights are the same, but the implicit ordering of the basis is different.

For a pseudoreal representation (which is self-dual), we also observe that the dual basis is ordered differently from the original basis.

This is essentially the difference between the representation of a field and is complex conjugate if it is in a pseudoreal representation (for instance the Higgs field).

Tech Notes
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  • Group Magic