Note on E representation in
S4 character table



2 irreducible representations of point group S4 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


S4 E S4 C2 (S4)3
A 1 1 1 1
B 1 -1 1 -1
E Ea
Eb
1
1
i
-i
-1
-1
-i
i


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