Matchete`
Matchete`

DynkinIndex

DynkinIndex[alg,rep]

returns the Dynkin index (trace normalization) of a representation.

Details and Options

  • The Dynkin indices are normalized to 1/2 for fundamental representations, which fixes all other representations.
  • The algebra argument must be a valid Alg[class, n] object.
  • Representations are labeled with a list of integers corresponding to the Dynkin coefficients of the highest weight in the representation.

Examples

Basic Examples  (1)

The Dynkin index (trace normalization) of the adjoint representation of SU(2)/A1 (note the use of SU[2] as short-hand for the algebra):

{2} is the Dynkin coefficients of the (highest weight of the) adjoint representation of SU(2).

Tech Notes
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  • Group Magic