Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 31' (N. 16.2.61)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
GM1
A1
GM1
1
1
1
1
1
1
GM2GM3
2E1E
GM2GM3
2
-1
-1
2
-1
-1
GM6GM6
EE
GM4GM4
2
-2
-2
-2
2
2
GM4GM5
1E2E
GM5GM6
2
1
1
-2
-1
-1
The notation used in this table is an extension to corepresentations of the following notations used for irreducible representations:
(1): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, based on Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love (1979) Kronecher Product Tables, 1, General Introduction and Tables of Irreducible Representations of Space groups. New York: IFI/Plenum, for the GM point.

Lists of unitary symmetry operations in the conjugacy classes

C1: 1
C2: 3+001
C3: 3-001
C4d1
C5d3+001
C6d3-001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM3GM4GM4GM5GM6
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0
0 1
)
2
(
0 -1 0
1 -1 0
0 0 1
)
(
(1+i3)/2 0
0 (1-i3)/2
)
3+001
1
(
ei2π/3 0
0 e-i2π/3
)
(
-1 0
0 -1
)
(
e-iπ/3 0
0 eiπ/3
)
3
(
-1 1 0
-1 0 0
0 0 1
)
(
(1-i3)/2 0
0 (1+i3)/2
)
3-001
1
(
e-i2π/3 0
0 ei2π/3
)
(
-1 0
0 -1
)
(
eiπ/3 0
0 e-iπ/3
)
4
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
5
(
0 -1 0
1 -1 0
0 0 1
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
d3+001
1
(
ei2π/3 0
0 e-i2π/3
)
(
1 0
0 1
)
(
ei2π/3 0
0 e-i2π/3
)
6
(
-1 1 0
-1 0 0
0 0 1
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
d3-001
1
(
e-i2π/3 0
0 ei2π/3
)
(
1 0
0 1
)
(
e-i2π/3 0
0 ei2π/3
)
7
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1'
1
(
0 1
1 0
)
(
0 -1
1 0
)
(
0 -1
1 0
)
8
(
0 -1 0
1 -1 0
0 0 1
)
(
(1+i3)/2 0
0 (1-i3)/2
)
3'+001
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 1
-1 0
)
(
0 ei2π/3
eiπ/3 0
)
9
(
-1 1 0
-1 0 0
0 0 1
)
(
(1-i3)/2 0
0 (1+i3)/2
)
3'-001
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 1
-1 0
)
(
0 e-i2π/3
e-iπ/3 0
)
10
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1'
1
(
0 1
1 0
)
(
0 1
-1 0
)
(
0 1
-1 0
)
11
(
0 -1 0
1 -1 0
0 0 1
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
d3'+001
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 -1
1 0
)
(
0 e-iπ/3
e-i2π/3 0
)
12
(
-1 1 0
-1 0 0
0 0 1
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
d3'-001
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 -1
1 0
)
(
0 eiπ/3
ei2π/3 0
)
k-Subgroupsmag
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