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Point Group Tables of C2v(mm2)

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Character Table of the group C2v(mm2)*
C2v(mm2)#12zmymxfunctions
A1Γ11111z,x2,y2,z2
A2Γ311-1-1xy,Jz
B1Γ21-11-1x,xz,Jy
B2Γ41-1-11y,yz,Jx



Subgroups of the group C2v(mm2)
SubgroupOrderIndex
C2v(mm2)41
C2(2)22
Cs(m)22
C1(1)14

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C2v(mm2)
C2v(mm2)A1A2B1B2
A1A1A2B1B2
A2·A1B2B1
B1··A1A2
B2···A1

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C2v(mm2)A1A2B1B2
[A1 x A1]1···
[A2 x A2]1···
[B1 x B1]1···
[B2 x B2]1···


Antisymmetrized Products of Irreps
C2v(mm2)A1A2B1B2
{A1 x A1}····
{A2 x A2}····
{B1 x B1}····
{B2 x B2}····


Irreps Decompositions
C2v(mm2)A1A2B1B2
V1·11
[V2]3111
[V3]3133
[V4]6333
A·111
[A2]3111
[A3]1333
[A4]6333
[V2]xV5355
[[V2]2]9444
{V2}·111
{A2}·111
{[V2]2}3444

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1A2B1B2
A1x·xx
A2·xxx
B1xxx·
B2xx·x

[ Note: x means allowed ]


Raman Selection Rules
RamanA1A2B1B2
A1xxxx
A2xxxx
B1xxxx
B2xxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C2v(mm2)
L2L+1A1A2B1B2
011···
131·11
252111
372122
493222
5113233
6134333
7154344
8175444
9195455
10216555


* 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.

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