Number of projective equivalence classes of irreducible linear representations

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Definition

Suppose G is a finite group and K is a field. The number of projective equivalence classes of irreducible linear representations is defined in the following equivalent ways:

  • It is the number of equivalence classes of irreducible linear representations of G over K under the action of the multiplicative group of one-dimensional representations.
  • It is the number of equivalence classes of irreducible linear representations under the equivalence relation of being projectively equivalent (see also projective representation).