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Irreducible representations of the Point Group m3 (No. 29)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
GM1-
1Au
GM1-
1
1
1
1
-1
-1
-1
-1
GM2+
1Eg
GM2+
1
1
-(1+i3)/2
-(1-i3)/2
1
1
-(1+i3)/2
-(1-i3)/2
GM2-
1Eu
GM2-
1
1
-(1+i3)/2
-(1-i3)/2
-1
-1
(1+i3)/2
(1-i3)/2
GM3+
2Eg
GM3+
1
1
-(1-i3)/2
-(1+i3)/2
1
1
-(1-i3)/2
-(1+i3)/2
GM3-
2Eu
GM3-
1
1
-(1-i3)/2
-(1+i3)/2
-1
-1
(1-i3)/2
(1+i3)/2
GM4+
Tg
GM4+
3
-1
0
0
3
-1
0
0
GM4-
Tu
GM4-
3
-1
0
0
-3
1
0
0
(1): Notation of the irreps according to Koster GF, Dimmok JO, Wheeler RG and Statz H, (1963) Properties of the thirty-two point groups, M.I.T. Press, Cambridge, Mass.
(2): Notation of the irreps according to Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): Notation of the irreps according to C. J. Bradley, A. P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon Press, Oxford, 1972) for the GM point.

Lists of symmetry operations in the conjugacy classes

C1: 1
C2: 2001, 2010, 2100
C3: 3--11-1, 3-1-1-1, 3--1-11, 3-111
C4: 3+1-1-1, 3+-1-11, 3+-11-1, 3+111
C5: -1
C6: m001, m010, m100
C7: -3--11-1, -3-1-1-1, -3--1-11, -3-111
C8: -3+1-1-1, -3+-1-11, -3+-11-1, -3+111

List of pairs of conjugated irreducible representations

(GM2+,GM3+)
(GM2-,GM3-)
Matrices of the representations of the group

N
General position
Seitz Symbol
GM1+(1)
GM1-(1)
GM2+(0)
GM2-(0)
GM3+(0)
GM3-(0)
GM4+(1)
GM4-(1)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
1
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 1
)
2
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
1
1
1
1
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
3
(
-1 0 0
0 1 0
0 0 -1
)
2010
1
1
1
1
1
1
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
4
(
1 0 0
0 -1 0
0 0 -1
)
2100
1
1
1
1
1
1
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
5
(
0 0 1
1 0 0
0 1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
6
(
0 0 1
-1 0 0
0 -1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
7
(
0 0 -1
-1 0 0
0 1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
8
(
0 0 -1
1 0 0
0 -1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
9
(
0 1 0
0 0 1
1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
10
(
0 -1 0
0 0 1
-1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
11
(
0 1 0
0 0 -1
-1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
12
(
0 -1 0
0 0 -1
1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
13
(
-1 0 0
0 -1 0
0 0 -1
)
1
1
-1
1
-1
1
-1
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 -1
)
14
(
1 0 0
0 1 0
0 0 -1
)
m001
1
-1
1
-1
1
-1
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
15
(
1 0 0
0 -1 0
0 0 1
)
m010
1
-1
1
-1
1
-1
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -1
)
16
(
-1 0 0
0 1 0
0 0 1
)
m100
1
-1
1
-1
1
-1
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
17
(
0 0 -1
-1 0 0
0 -1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
18
(
0 0 -1
1 0 0
0 1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
19
(
0 0 1
1 0 0
0 -1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
20
(
0 0 1
-1 0 0
0 1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
21
(
0 -1 0
0 0 -1
-1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
22
(
0 1 0
0 0 -1
1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
23
(
0 -1 0
0 0 1
1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
24
(
0 1 0
0 0 1
-1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
k-Subgroupsmag
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