Multiplication Table of irreducible representations of the group C2(2)
C2(2)
A
B
A
A
B
B
·
A
[ Note: the table is symmetric ]
Symmetrized Products of Irreps
C2(2)
A
B
[A x A]
1
·
[B x B]
1
·
Antisymmetrized Products of Irreps
C2(2)
A
B
{A x A}
·
·
{B x B}
·
·
Irreps Decompositions
C2(2)
A
B
V
1
2
[V2]
4
2
[V3]
4
6
[V4]
9
6
A
1
2
[A2]
4
2
[A3]
4
6
[A4]
9
6
[V2]xV
8
10
[[V2]2]
13
8
{V2}
1
2
{A2}
1
2
{[V2]2}
7
8
V ≡ the vector representation
A ≡ the axial representation
IR Selection Rules
IR
A
B
A
x
x
B
x
x
[ Note: x means allowed ]
Raman Selection Rules
Raman
A
B
A
x
x
B
x
x
[ Note: x means allowed ]
Irreps
Dimensions
Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C2(2)
L
2L+1
A
B
0
1
1
·
1
3
1
2
2
5
3
2
3
7
3
4
4
9
5
4
5
11
5
6
6
13
7
6
7
15
7
8
8
17
9
8
9
19
9
10
10
21
11
10
*
C. J. Bradley and A. P. Cracknell (1972)
The Mathematical Theory of Symmetry in Solids
Clarendon Press - Oxford
*
Simon L. Altmann and Peter Herzig (1994).
Point-Group Theory Tables.
Oxford Science Publications.