Matchete`
Matchete`

Generators

Generators[alg,rep]

returns Hermitian and normalized generators of the representation.

Details and Options

  • The generators are returned as a rank-3 tensor (SparseArray).
  • The basis used for the adjoint index is common across generators of all representations of the Lie algebra. All representation bases are consistent also with the tensors from StructureConstants and InvariantTensors.
  • The generators are normalized consistently with DynkinIndex.
  • 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 generators of the fundamental representation of SU(2)/A1 (note the use of SU[2] as short-hand for the algebra):

{1} is the Dynkin coefficients of the (highest weight of the) fundamental representation of SU(2). While the generators are ordered differently form the common choice based on the Pauli matrices, they are internally consistent with generators produced for all other representations.

Tech Notes
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  • Group Magic