Matchete`
Matchete`

Casimir2

Casimir2[alg,rep]

returns the quadratic Casimir of a representation.

Details and Options

  • The normalization of the quadratic Casimir operator follows from the DynkinIndex. 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 quadratic Casimir of the two-index symmetric representation of SU(3)/A2 (note the use of SU[3] as short-hand for the algebra):

{2, 0} is the Dynkin coefficients of the (highest weight of the) two-index symmetric representation of SU(3).

Tech Notes
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  • Group Magic