Matchete`
Matchete`

FSIndicator

FSIndicator[alg,rep]

returns the Frobenius-Schur indicator of a representation.

Details and Options

  • The indicator is +1 for real representations, 0 for complex representations, and -1 for pseudoreal 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  (3)

The Frobenius-Schur indicator of fundamental representation ({1, 0}) of SU(3)/A2 (note the use of SU[3] as short-hand for the algebra) is 0, as the representation is complex :

The Frobenius-Schur indicator of fundamental representation ({1, 0, 0}) of Sp(4)/C2 is -1, as the representation is pseudoreal :

The Frobenius-Schur indicator of fundamental representation ({1, 0}) of SO(5)/B2 is +1, as the representation is real :

Tech Notes
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  • Group Magic