GTReality

GTReality[classes,characters]
estimates if a representation is potentially real, essentially complex or pseudo-real from the theorem of Frobenius and Schur.

DetailsDetails

  • Let be a representation of a finite group of order with characters . Then, the reality of a representation can be estimated from the sum over (Theorem of Frobenius and Schur).
  • The following option can be given:
  • GOFastGOFastValueSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 8.7

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First, load the package:

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As an example, the irreducible representations of the group are discussed. The character table is given by:

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The representation is potentially real.

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The representations and are essentially complex.

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