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Point Group Tables of Ci(-1)

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Character Table of the group Ci(-1) *
Ci(-1)#1-1functions
AgΓ1+11x2,y2,z2,xy,xz,yz,Jx,Jy,Jz
AuΓ1-1-1x,y,z



Subgroups of the group Ci(-1)
SubgroupOrderIndex
Ci(-1)21
C1(1)12

[ Subduction tables ]

Multiplication Table of irreducible representations of the group Ci(-1)
Ci(-1)AgAu
AgAgAu
AuAg

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
Ci(-1)AgAu
[Ag x Ag]1·
[Au x Au]1·


Antisymmetrized Products of Irreps
Ci(-1)AgAu
{Ag x Ag}··
{Au x Au}··


Irreps Decompositions
Ci(-1)AgAu
V·3
[V2]6·
[V3]·10
[V4]15·
A3·
[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
IRAgAu
Agx
Aux

[ Note: x means allowed ]


Raman Selection Rules
RamanAgAu
Agx
Aux

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group Ci(-1)
L2L+1AgAu
011·
13·3
255·
37·7
499·
511·11
61313·
715·15
81717·
919·19
102121·



* 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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