Note on E representations in
C5 character table



4 irreducible representations of point group C5 have complex values. 2 two-dimensional real-valued representations E can be constructed as direct sum of the 2 pairs complex plus conjugate complex irreducible representation.

E1 = E1a ⊕ E1b
E2 = E2a ⊕ E2b


ε=exp(2πi/5)
C5 E C5 (C5)2 (C5)3 (C5)4
A 1 1 1 1 1
E1 E1a
E1b
1
1
ε*
ε*
ε2*
ε2*
ε2*
ε2*
ε*
ε*
E2 E2a
E2b
1
1
ε2*
ε2*
ε*
ε*
ε*
ε*
ε2*
ε2*


Obviously the E representations are reducible. Nevertheless the E representations are treated often as irreducible representations and are called real-valued or pseudo irreducible representations. 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