GroupTheory`
GroupTheory`

GTReality

GTReality[classes,characters]

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

Details and Options

  • 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:
  • GOFast GOFastValueSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 8.7

Examples

open allclose all

Basic Examples  (1)

First, load the package:

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

The representation is potentially real.

The representations and are essentially complex.

Options  (2)

GOFast  (2)

The evaluation time can be decreased, using GOFastTrue.

If GOFastFalse is used, a check of the input will be performed.