Multiplication Table of irreducible representations of the group C1(1)
C1(1)
A
A
A
[ Note: the table is symmetric ]
Symmetrized Products of Irreps
C1(1)
A
[A x A]
1
Antisymmetrized Products of Irreps
C1(1)
A
{A x A}
·
Irreps Decompositions
C1(1)
A
V
3
[V2]
6
[V3]
10
[V4]
15
A
3
[A2]
6
[A3]
10
[A4]
15
[V2]xV
18
[[V2]2]
21
{V2}
3
{A2}
3
{[V2]2}
15
V ≡ the vector representation
A ≡ the axial representation
IR Selection Rules
IR
A
A
x
[ Note: x means allowed ]
Raman Selection Rules
Raman
A
A
x
[ Note: x means allowed ]
Irreps
Dimensions
Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C1(1)
L
2L+1
A
0
1
1
1
3
3
2
5
5
3
7
7
4
9
9
5
11
11
6
13
13
7
15
15
8
17
17
9
19
19
10
21
21
*
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.
Point Group Tables
