Note on E representation in
C3 character table



2 irreducible representations of point group C3 have complex values. A two-dimensional real-valued representation E can be constructed as direct sum of the pair complex plus conjugate complex irreducible representation.

E = Ea ⊕ Eb


ε=exp(2πi/3)
C3 E C3 (C3)2
A 1 1 1
E Ea
Eb
1
1
ε*
ε*
ε*
ε*


Obviously the E representation is reducible. Nevertheless the E representation is treated often as irreducible representation and is called real-valued or pseudo irreducible representation. One should keep in mind that general statements for character tables fail for real-valued representations. For example:



Last update August, 12th 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement