Determine the irrep content for the equivalent reducible \(S_{3}\) representations \(\Gamma^{(4)}\) and \(\Gamma^{(5)}\) of Fig. 2.4 .

Data from Fig.  2.4

Transcribed Image Text:

F(1) (2) 1 (3) (4) r(5) (6) 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 100 (1) 1 1 ( 9 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 001 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 (123) 1 1 -1/2 3/2 -3/2-1/2) 0 -1/2 03/2-1/2) 3/2 (0 0 1 100 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 (321) 1 1 (-1/2-3/2 3/2-1/2 1 0 0 ) 0-1/2/3/2 0 1 0) 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 3/2-1/2 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 (23) 1 T (661 9 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 -1 0 1 0 0 001 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0,