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Point Group Tables of C3i(-3)

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Character Table of the group C3i(-3) *
C3i(-3)#13+3--1-3+-3-functions
AgΓ1+111111x2+y2,z2,Jz
1Eg
2Eg
Γ3+
Γ2+
1
1
w2
w
w
w2
1
1
w2
w
w
w2
(xz,yz),(x2-y2,xy),(Jx,Jy)
AuΓ1-111-1-1-1z
1Eu
2Eu
Γ3-
Γ2-
1
1
w2
w
w
w2
-1
-1
-w2
-w
-w
-w2
(x,y)

w = exp(2iπ/3)



Subgroups of the group C3i(-3)
SubgroupOrderIndex
C3i(-3)61
C3(3)32
Ci(-1)23
C1(1)16

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C3i(-3)
C3i(-3)AgAu1Eg1Eu2Eg2Eu
AgAgAu1Eg1Eu2Eg2Eu
AuAg1Eu1Eg2Eu2Eg
1Eg2Eg2EuAgAu
1Eu2EgAuAg
2Eg1Eg1Eu
2Eu1Eg

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C3i(-3)AgAu1Eg1Eu2Eg2Eu
[Ag x Ag]1·····
[Au x Au]1·····
[1Eg x 1Eg]····1·
[1Eu x 1Eu]····1·
[2Eg x 2Eg]··1···
[2Eu x 2Eu]··1···


Antisymmetrized Products of Irreps
C3i(-3)AgAu1Eg1Eu2Eg2Eu
{Ag x Ag}······
{Au x Au}······
{1Eg x 1Eg}······
{1Eu x 1Eu}······
{2Eg x 2Eg}······
{2Eu x 2Eu}······


Irreps Decompositions
C3i(-3)AgAu1Eg1Eu2Eg2Eu
V·1·1·1
[V2]2·2·2·
[V3]·4·3·3
[V4]5·5·5·
A1·1·1·
[A2]2·2·2·
[A3]4·3·3·
[A4]5·5·5·
[V2]xV·6·6·6
[[V2]2]7·7·7·
{V2}1·1·1·
{A2}1·1·1·
{[V2]2}5·5·5·

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRAgAu1Eg1Eu2Eg2Eu
Agxxx
Auxxx
1Egxxx
1Euxxx
2Egxxx
2Euxxx

[ Note: x means allowed ]


Raman Selection Rules
RamanAgAu1Eg1Eu2Eg2Eu
Agxxx
Auxxx
1Egxxx
1Euxxx
2Egxxx
2Euxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C3i(-3)
L2L+1AgAu1Eg1Eu2Eg2Eu
011·····
13·1·1·1
251·2·2·
37·3·2·2
493·3·3·
511·3·4·4
6135·4·4·
715·5·5·5
8175·6·6·
919·7·6·6
10217·7·7·



* George F. Koster, John O. Dimmock, Robert G. Wheeler, Hermann Statz (1963). Properties of the thirty-two point groups. Published by the M.I.T. press, Cambridge, Massachusetts.
* Simon L. Altmann and Peter Herzig (1994). Point-Group Theory Tables. Oxford Science Publications.


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