Matchete`
Matchete`

RepresentationWeights

RepresentationWeights[alg,rep]

returns the weights of a representation with multiplicity.

Details and Options

  • The resulting association uses representation uses the Dynkin coefficients of the weights for its keys with multiplicities of the weights in the representation as values.
  • 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.
  • The following options can be given:
  • Levels Falseindicates whether the weight should be sorted by their level in the decend from the heighest weight.
  • The levels of a weight is obtain in the process of finding the weights of a representation by successively subtracting simple roots from the highest weight of the representation.

Examples

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Basic Examples  (1)

The dimension 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).

Options  (1)

Levels  (1)

With the Levels option, we may obtain the level of each root in the representation. In the two-index symmetric representation of SU(3) only the third level has multiple roots:

Tech Notes
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  • Group Magic