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Irreducible corepresentations of the Projective Magnetic Point Group 4'm'm


Table of characters of the unitary symmetry operations


1
2
d2
m1-1
dm1-1
m11
dm11
d1
A1
1
1
1
1
1
A2
1
1
-1
-1
1
B2B1
2
-2
0
0
2
E
2
0
0
0
-2

Multiplication table of the symmetry operations


1
2
m1-1
m11
d1
d2
dm1-1
dm11
4+'
4-'
m'10
m'01
d4+'
d4-'
dm'10
dm'01
1
1
2
m1-1
m11
d1
d2
dm1-1
dm11
4+'
4-'
m'10
m'01
d4+'
d4-'
dm'10
dm'01
2
2
d1
dm11
m1-1
d2
1
m11
dm1-1
d4-'
4+'
m'01
dm'10
4-'
d4+'
dm'01
m'10
m1-1
m1-1
m11
d1
d2
dm1-1
dm11
1
2
m'01
dm'10
4-'
d4+'
dm'01
m'10
d4-'
4+'
m11
m11
dm1-1
2
d1
dm11
m1-1
d2
1
m'10
m'01
d4+'
d4-'
dm'10
dm'01
4+'
4-'
d1
d1
d2
dm1-1
dm11
1
2
m1-1
m11
d4+'
d4-'
dm'10
dm'01
4+'
4-'
m'10
m'01
d2
d2
1
m11
dm1-1
2
d1
dm11
m1-1
4-'
d4+'
dm'01
m'10
d4-'
4+'
m'01
dm'10
dm1-1
dm1-1
dm11
1
2
m1-1
m11
d1
d2
dm'01
m'10
d4-'
4+'
m'01
dm'10
4-'
d4+'
dm11
dm11
m1-1
d2
1
m11
dm1-1
2
d1
dm'10
dm'01
4+'
4-'
m'10
m'01
d4+'
d4-'
4+'
4+'
d4-'
dm'10
m'01
d4+'
4-'
m'10
dm'01
d2
d1
dm11
dm1-1
2
1
m11
m1-1
4-'
4-'
4+'
m'01
m'10
d4-'
d4+'
dm'01
dm'10
d1
2
m1-1
dm11
1
d2
dm1-1
m11
m'10
m'10
dm'01
4+'
d4-'
dm'10
m'01
d4+'
4-'
m1-1
dm11
1
d2
dm1-1
m11
d1
2
m'01
m'01
m'10
d4-'
d4+'
dm'01
dm'10
4-'
4+'
dm11
dm1-1
2
1
m11
m1-1
d2
d1
d4+'
d4+'
4-'
m'10
dm'01
4+'
d4-'
dm'10
m'01
2
1
m11
m1-1
d2
d1
dm11
dm1-1
d4-'
d4-'
d4+'
dm'01
dm'10
4-'
4+'
m'01
m'10
1
d2
dm1-1
m11
d1
2
m1-1
dm11
dm'10
dm'10
m'01
d4+'
4-'
m'10
dm'01
4+'
d4-'
dm1-1
m11
d1
2
m1-1
dm11
1
d2
dm'01
dm'01
dm'10
4-'
4+'
m'01
m'10
d4-'
d4+'
m11
m1-1
d2
d1
dm11
dm1-1
2
1

Table of projective phases in group multiplication


1
2
m1-1
m11
d1
d2
dm1-1
dm11
4+'
4-'
m'10
m'01
d4+'
d4-'
dm'10
dm'01
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
m1-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
m11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
dm1-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
dm11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4+'
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4-'
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
m'10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
m'01
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d4+'
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d4-'
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
dm'10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
dm'01
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolA1A2B2B1E
1
(
1 0
0 1
)
(
1 0
0 1
)
1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
2
(
-1 0
0 -1
)
(
-i 0
0 i
)
2
1
1
(
-1 0
0 -1
)
(
-i 0
0 i
)
3
(
0 1
1 0
)
(
0 e3iπ/4
eiπ/4 0
)
m1-1
1
-1
(
1 0
0 -1
)
(
0 i
i 0
)
4
(
0 -1
-1 0
)
(
0 e-3iπ/4
e-iπ/4 0
)
m11
1
-1
(
-1 0
0 1
)
(
0 -1
1 0
)
5
(
1 0
0 1
)
(
-1 0
0 -1
)
d1
1
1
(
1 0
0 1
)
(
-1 0
0 -1
)
6
(
-1 0
0 -1
)
(
i 0
0 -i
)
d2
1
1
(
-1 0
0 -1
)
(
i 0
0 -i
)
7
(
0 1
1 0
)
(
0 e-iπ/4
e-3iπ/4 0
)
dm1-1
1
-1
(
1 0
0 -1
)
(
0 -i
-i 0
)
8
(
0 -1
-1 0
)
(
0 eiπ/4
e3iπ/4 0
)
dm11
1
-1
(
-1 0
0 1
)
(
0 1
-1 0
)
9
(
0 -1
1 0
)
(
e-iπ/4 0
0 eiπ/4
)
4+'
-1
1
(
0 -1
1 0
)
(
0 e-3iπ/4
e-iπ/4 0
)
10
(
0 1
-1 0
)
(
eiπ/4 0
0 e-iπ/4
)
4-'
-1
1
(
0 1
-1 0
)
(
0 e3iπ/4
eiπ/4 0
)
11
(
-1 0
0 1
)
(
0 -i
-i 0
)
m'10
-1
-1
(
0 1
1 0
)
(
e-3iπ/4 0
0 e3iπ/4
)
12
(
1 0
0 -1
)
(
0 -1
1 0
)
m'01
-1
-1
(
0 -1
-1 0
)
(
e-iπ/4 0
0 eiπ/4
)
13
(
0 -1
1 0
)
(
e3iπ/4 0
0 e-3iπ/4
)
d4+'
-1
1
(
0 -1
1 0
)
(
0 eiπ/4
e3iπ/4 0
)
14
(
0 1
-1 0
)
(
e-3iπ/4 0
0 e3iπ/4
)
d4-'
-1
1
(
0 1
-1 0
)
(
0 e-iπ/4
e-3iπ/4 0
)
15
(
-1 0
0 1
)
(
0 i
i 0
)
dm'10
-1
-1
(
0 1
1 0
)
(
eiπ/4 0
0 e-iπ/4
)
16
(
1 0
0 -1
)
(
0 1
-1 0
)
dm'01
-1
-1
(
0 -1
-1 0
)
(
e3iπ/4 0
0 e-3iπ/4
)
k-Subgroupsmag
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