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


Table of characters of the unitary symmetry operations


1
4+
2
4-
d1
d4+
d2
d4-
A
1
1
1
1
1
1
1
1
B
1
-1
1
-1
1
-1
1
-1
2E
1
i
-1
-i
1
i
-1
-i
1E
1
-i
-1
i
1
-i
-1
i
1E1
1
eiπ/4
i
e-iπ/4
-1
e-3iπ/4
-i
e3iπ/4
1E2
1
e-3iπ/4
i
e3iπ/4
-1
eiπ/4
-i
e-iπ/4
2E2
1
e3iπ/4
-i
e-3iπ/4
-1
e-iπ/4
i
eiπ/4
2E1
1
e-iπ/4
-i
eiπ/4
-1
e3iπ/4
i
e-3iπ/4

Multiplication table of the symmetry operations


1
4+
2
4-
d1
d4+
d2
d4-
m'10
m'1-1
m'01
m'11
dm'10
dm'1-1
dm'01
dm'11
1
1
4+
2
4-
d1
d4+
d2
d4-
m'10
m'1-1
m'01
m'11
dm'10
dm'1-1
dm'01
dm'11
4+
4+
2
d4-
1
d4+
d2
4-
d1
m'11
dm'10
m'1-1
m'01
dm'11
m'10
dm'1-1
dm'01
2
2
d4-
d1
4+
d2
4-
1
d4+
m'01
dm'11
dm'10
m'1-1
dm'01
m'11
m'10
dm'1-1
4-
4-
1
4+
d2
d4-
d1
d4+
2
dm'1-1
m'01
m'11
m'10
m'1-1
dm'01
dm'11
dm'10
d1
d1
d4+
d2
d4-
1
4+
2
4-
dm'10
dm'1-1
dm'01
dm'11
m'10
m'1-1
m'01
m'11
d4+
d4+
d2
4-
d1
4+
2
d4-
1
dm'11
m'10
dm'1-1
dm'01
m'11
dm'10
m'1-1
m'01
d2
d2
4-
1
d4+
2
d4-
d1
4+
dm'01
m'11
m'10
dm'1-1
m'01
dm'11
dm'10
m'1-1
d4-
d4-
d1
d4+
2
4-
1
4+
d2
m'1-1
dm'01
dm'11
dm'10
dm'1-1
m'01
m'11
m'10
m'10
m'10
dm'1-1
dm'01
m'11
dm'10
m'1-1
m'01
dm'11
1
d4+
d2
4-
d1
4+
2
d4-
m'1-1
m'1-1
m'01
m'11
dm'10
dm'1-1
dm'01
dm'11
m'10
d4-
1
4+
2
4-
d1
d4+
d2
m'01
m'01
m'11
m'10
m'1-1
dm'01
dm'11
dm'10
dm'1-1
2
4-
1
4+
d2
d4-
d1
d4+
m'11
m'11
m'10
dm'1-1
m'01
dm'11
dm'10
m'1-1
dm'01
4+
d2
4-
1
d4+
2
d4-
d1
dm'10
dm'10
m'1-1
m'01
dm'11
m'10
dm'1-1
dm'01
m'11
d1
4+
2
d4-
1
d4+
d2
4-
dm'1-1
dm'1-1
dm'01
dm'11
m'10
m'1-1
m'01
m'11
dm'10
4-
d1
d4+
d2
d4-
1
4+
2
dm'01
dm'01
dm'11
dm'10
dm'1-1
m'01
m'11
m'10
m'1-1
d2
d4-
d1
d4+
2
4-
1
4+
dm'11
dm'11
dm'10
m'1-1
dm'01
m'11
m'10
dm'1-1
m'01
d4+
2
d4-
d1
4+
d2
4-
1

Table of projective phases in group multiplication


1
4+
2
4-
d1
d4+
d2
d4-
m'10
m'1-1
m'01
m'11
dm'10
dm'1-1
dm'01
dm'11
1
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
2
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
d1
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
d2
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
m'10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
m'1-1
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
m'11
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'1-1
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
dm'11
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 symbolAB2E1E1E11E22E22E1
1
(
1 0
0 1
)
(
1 0
0 1
)
1
1
1
1
1
1
1
1
1
2
(
0 -1
1 0
)
(
e-iπ/4 0
0 eiπ/4
)
4+
1
-1
i
-i
eiπ/4
e-3iπ/4
e3iπ/4
e-iπ/4
3
(
-1 0
0 -1
)
(
-i 0
0 i
)
2
1
1
-1
-1
i
i
-i
-i
4
(
0 1
-1 0
)
(
eiπ/4 0
0 e-iπ/4
)
4-
1
-1
-i
i
e-iπ/4
e3iπ/4
e-3iπ/4
eiπ/4
5
(
1 0
0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
-1
-1
-1
-1
6
(
0 -1
1 0
)
(
e3iπ/4 0
0 e-3iπ/4
)
d4+
1
-1
i
-i
e-3iπ/4
eiπ/4
e-iπ/4
e3iπ/4
7
(
-1 0
0 -1
)
(
i 0
0 -i
)
d2
1
1
-1
-1
-i
-i
i
i
8
(
0 1
-1 0
)
(
e-3iπ/4 0
0 e3iπ/4
)
d4-
1
-1
-i
i
e3iπ/4
e-iπ/4
eiπ/4
e-3iπ/4
9
(
-1 0
0 1
)
(
0 -i
-i 0
)
m'10
-1
-1
-1
-1
-1
-1
-1
-1
10
(
0 1
1 0
)
(
0 e3iπ/4
eiπ/4 0
)
m'1-1
-1
1
-i
i
eiπ/4
e-3iπ/4
e3iπ/4
e-iπ/4
11
(
1 0
0 -1
)
(
0 -1
1 0
)
m'01
-1
-1
1
1
i
i
-i
-i
12
(
0 -1
-1 0
)
(
0 e-3iπ/4
e-iπ/4 0
)
m'11
-1
1
i
-i
e3iπ/4
e-iπ/4
eiπ/4
e-3iπ/4
13
(
-1 0
0 1
)
(
0 i
i 0
)
dm'10
-1
-1
-1
-1
1
1
1
1
14
(
0 1
1 0
)
(
0 e-iπ/4
e-3iπ/4 0
)
dm'1-1
-1
1
-i
i
e-3iπ/4
eiπ/4
e-iπ/4
e3iπ/4
15
(
1 0
0 -1
)
(
0 1
-1 0
)
dm'01
-1
-1
1
1
-i
-i
i
i
16
(
0 -1
-1 0
)
(
0 eiπ/4
e3iπ/4 0
)
dm'11
-1
1
i
-i
e-iπ/4
e3iπ/4
e-3iπ/4
eiπ/4
k-Subgroupsmag
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