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Irreducible corepresentations of the Projective Magnetic Point Group 4π/2mm


Table of characters of the unitary symmetry operations


1
4+
2
4-
m10
dm01
m1-1
m11
m01
dm10
d1
d4+
d2
d4-
dm1-1
dm11
2EB
2
√2e3iπ/4
0
√2e-3iπ/4
0
0
0
2
√2e3iπ/4
0
√2e-3iπ/4
0
1EA
2
√2e-iπ/4
0
√2eiπ/4
0
0
0
2
√2e-iπ/4
0
√2eiπ/4
0
2E2'
1
e3iπ/4
-i
e-3iπ/4
i
i
-i
-1
e-iπ/4
i
eiπ/4
-i
2E2''
1
e3iπ/4
-i
e-3iπ/4
-i
-i
i
-1
e-iπ/4
i
eiπ/4
i
2E1'
1
e-iπ/4
-i
eiπ/4
i
-i
-i
-1
e3iπ/4
i
e-3iπ/4
i
2E1''
1
e-iπ/4
-i
eiπ/4
-i
i
i
-1
e3iπ/4
i
e-3iπ/4
-i
1E11E2
2
0
2i
0
0
0
0
-2
0
-2i
0
0

Multiplication table of the symmetry operations


1
4+
2
4-
m10
m1-1
m01
m11
d1
d4+
d2
d4-
dm10
dm1-1
dm01
dm11
1
1
4+
2
4-
m10
m1-1
m01
m11
d1
d4+
d2
d4-
dm10
dm1-1
dm01
dm11
4+
4+
2
d4-
1
m11
dm10
m1-1
m01
d4+
d2
4-
d1
dm11
m10
dm1-1
dm01
2
2
d4-
d1
4+
m01
dm11
dm10
m1-1
d2
4-
1
d4+
dm01
m11
m10
dm1-1
4-
4-
1
4+
d2
dm1-1
m01
m11
m10
d4-
d1
d4+
2
m1-1
dm01
dm11
dm10
m10
m10
dm1-1
dm01
m11
d1
4+
2
d4-
dm10
m1-1
m01
dm11
1
d4+
d2
4-
m1-1
m1-1
m01
m11
dm10
4-
d1
d4+
d2
dm1-1
dm01
dm11
m10
d4-
1
4+
2
m01
m01
m11
m10
m1-1
d2
d4-
d1
d4+
dm01
dm11
dm10
dm1-1
2
4-
1
4+
m11
m11
m10
dm1-1
m01
d4+
2
d4-
d1
dm11
dm10
m1-1
dm01
4+
d2
4-
1
d1
d1
d4+
d2
d4-
dm10
dm1-1
dm01
dm11
1
4+
2
4-
m10
m1-1
m01
m11
d4+
d4+
d2
4-
d1
dm11
m10
dm1-1
dm01
4+
2
d4-
1
m11
dm10
m1-1
m01
d2
d2
4-
1
d4+
dm01
m11
m10
dm1-1
2
d4-
d1
4+
m01
dm11
dm10
m1-1
d4-
d4-
d1
d4+
2
m1-1
dm01
dm11
dm10
4-
1
4+
d2
dm1-1
m01
m11
m10
dm10
dm10
m1-1
m01
dm11
1
d4+
d2
4-
m10
dm1-1
dm01
m11
d1
4+
2
d4-
dm1-1
dm1-1
dm01
dm11
m10
d4-
1
4+
2
m1-1
m01
m11
dm10
4-
d1
d4+
d2
dm01
dm01
dm11
dm10
dm1-1
2
4-
1
4+
m01
m11
m10
m1-1
d2
d4-
d1
d4+
dm11
dm11
dm10
m1-1
dm01
4+
d2
4-
1
m11
m10
dm1-1
m01
d4+
2
d4-
d1

Table of projective phases in group multiplication


1
4+
2
4-
m10
m1-1
m01
m11
d1
d4+
d2
d4-
dm10
dm1-1
dm01
dm11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4+
1
1
1
1
e3iπ/4
e-iπ/4
e-iπ/4
e-iπ/4
1
1
1
1
e3iπ/4
e-iπ/4
e-iπ/4
e-iπ/4
2
1
1
1
1
i
i
-i
-i
1
1
1
1
i
i
-i
-i
4-
1
1
1
1
eiπ/4
eiπ/4
eiπ/4
e-3iπ/4
1
1
1
1
eiπ/4
eiπ/4
eiπ/4
e-3iπ/4
m10
1
e-iπ/4
-i
e-3iπ/4
1
eiπ/4
i
e3iπ/4
1
e-iπ/4
-i
e-3iπ/4
1
eiπ/4
i
e3iπ/4
m1-1
1
e-iπ/4
-i
eiπ/4
e-iπ/4
1
eiπ/4
i
1
e-iπ/4
-i
eiπ/4
e-iπ/4
1
eiπ/4
i
m01
1
e-iπ/4
i
eiπ/4
-i
e-iπ/4
1
eiπ/4
1
e-iπ/4
i
eiπ/4
-i
e-iπ/4
1
eiπ/4
m11
1
e3iπ/4
i
eiπ/4
e-3iπ/4
-i
e-iπ/4
1
1
e3iπ/4
i
eiπ/4
e-3iπ/4
-i
e-iπ/4
1
d1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d4+
1
1
1
1
e3iπ/4
e-iπ/4
e-iπ/4
e-iπ/4
1
1
1
1
e3iπ/4
e-iπ/4
e-iπ/4
e-iπ/4
d2
1
1
1
1
i
i
-i
-i
1
1
1
1
i
i
-i
-i
d4-
1
1
1
1
eiπ/4
eiπ/4
eiπ/4
e-3iπ/4
1
1
1
1
eiπ/4
eiπ/4
eiπ/4
e-3iπ/4
dm10
1
e-iπ/4
-i
e-3iπ/4
1
eiπ/4
i
e3iπ/4
1
e-iπ/4
-i
e-3iπ/4
1
eiπ/4
i
e3iπ/4
dm1-1
1
e-iπ/4
-i
eiπ/4
e-iπ/4
1
eiπ/4
i
1
e-iπ/4
-i
eiπ/4
e-iπ/4
1
eiπ/4
i
dm01
1
e-iπ/4
i
eiπ/4
-i
e-iπ/4
1
eiπ/4
1
e-iπ/4
i
eiπ/4
-i
e-iπ/4
1
eiπ/4
dm11
1
e3iπ/4
i
eiπ/4
e-3iπ/4
-i
e-iπ/4
1
1
e3iπ/4
i
eiπ/4
e-3iπ/4
-i
e-iπ/4
1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbol2EB1EA2E2'2E2''2E1'2E1''1E11E2
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
1
1
1
1
(
 1 0
 0 1
)
2
(
  0 -1
  1  0
)
(
 e-iπ/4  0
  0  eiπ/4
)
4+
(
  i  0
  0 -1
)
(
 -i  0
  0  1
)
e3iπ/4
e3iπ/4
e-iπ/4
e-iπ/4
(
 e-3iπ/4  0
  0  eiπ/4
)
3
(
 -1  0
  0 -1
)
(
 -i  0
  0  i
)
2
(
 -1  0
  0  1
)
(
 -1  0
  0  1
)
-i
-i
-i
-i
(
 i 0
 0 i
)
4
(
  0  1
 -1  0
)
(
  eiπ/4  0
  0 e-iπ/4
)
4-
(
 -i  0
  0 -1
)
(
 i 0
 0 1
)
e-3iπ/4
e-3iπ/4
eiπ/4
eiπ/4
(
 e3iπ/4  0
  0 e-iπ/4
)
5
(
 -1  0
  0  1
)
(
  0 -i
 -i  0
)
m10
(
 0 1
 1 0
)
(
 0 1
 1 0
)
i
-i
i
-i
(
  0 -1
  1  0
)
6
(
 0 1
 1 0
)
(
  0 e3iπ/4
  eiπ/4  0
)
m1-1
(
  0 e-3iπ/4
  e3iπ/4  0
)
(
  0  eiπ/4
 e-iπ/4  0
)
i
-i
-i
i
(
 0 i
 i 0
)
7
(
  1  0
  0 -1
)
(
  0 -1
  1  0
)
m01
(
  0  i
 -i  0
)
(
  0  i
 -i  0
)
-i
i
-i
i
(
  0 -1
  1  0
)
8
(
  0 -1
 -1  0
)
(
  0 e-3iπ/4
  e-iπ/4  0
)
m11
(
  0 e-iπ/4
  eiπ/4  0
)
(
  0  e3iπ/4
 e-3iπ/4  0
)
i
-i
-i
i
(
  0 -i
 -i  0
)
9
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
d1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
-1
-1
-1
-1
(
 -1  0
  0 -1
)
10
(
  0 -1
  1  0
)
(
  e3iπ/4  0
  0 e-3iπ/4
)
d4+
(
  i  0
  0 -1
)
(
 -i  0
  0  1
)
e-iπ/4
e-iπ/4
e3iπ/4
e3iπ/4
(
  eiπ/4  0
  0 e-3iπ/4
)
11
(
 -1  0
  0 -1
)
(
  i  0
  0 -i
)
d2
(
 -1  0
  0  1
)
(
 -1  0
  0  1
)
i
i
i
i
(
 -i  0
  0 -i
)
12
(
  0  1
 -1  0
)
(
 e-3iπ/4  0
  0  e3iπ/4
)
d4-
(
 -i  0
  0 -1
)
(
 i 0
 0 1
)
eiπ/4
eiπ/4
e-3iπ/4
e-3iπ/4
(
 e-iπ/4  0
  0 e3iπ/4
)
13
(
 -1  0
  0  1
)
(
 0 i
 i 0
)
dm10
(
 0 1
 1 0
)
(
 0 1
 1 0
)
-i
i
-i
i
(
  0  1
 -1  0
)
14
(
 0 1
 1 0
)
(
  0  e-iπ/4
 e-3iπ/4  0
)
dm1-1
(
  0 e-3iπ/4
  e3iπ/4  0
)
(
  0  eiπ/4
 e-iπ/4  0
)
-i
i
i
-i
(
  0 -i
 -i  0
)
15
(
  1  0
  0 -1
)
(
  0  1
 -1  0
)
dm01
(
  0  i
 -i  0
)
(
  0  i
 -i  0
)
i
-i
i
-i
(
  0  1
 -1  0
)
16
(
  0 -1
 -1  0
)
(
  0  eiπ/4
 e3iπ/4  0
)
dm11
(
  0 e-iπ/4
  eiπ/4  0
)
(
  0  e3iπ/4
 e-3iπ/4  0
)
-i
i
i
-i
(
 0 i
 i 0
)
k-Subgroupsmag
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