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Irreducible corepresentations of the Projective Magnetic Point Group 3m


Table of characters of the unitary symmetry operations


1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
A1
1
1
1
1
1
1
A2
1
1
-1
1
1
-1
E
2
-1
0
2
-1
0
1E
1
-1
i
-1
1
-i
2E
1
-1
-i
-1
1
i
E1
2
1
0
-2
-1
0

Multiplication table of the symmetry operations


1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
1
1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
3+
3+
d3-
1
dm21
dm1-1
dm12
d3+
3-
d1
m21
m1-1
m12
3-
3-
1
d3+
dm12
dm21
dm1-1
d3-
d1
3+
m12
m21
m1-1
m1-1
m1-1
dm12
dm21
d1
3+
3-
dm1-1
m12
m21
1
d3+
d3-
m12
m12
dm21
dm1-1
3-
d1
3+
dm12
m21
m1-1
d3-
1
d3+
m21
m21
dm1-1
dm12
3+
3-
d1
dm21
m1-1
m12
d3+
d3-
1
d1
d1
d3+
d3-
dm1-1
dm12
dm21
1
3+
3-
m1-1
m12
m21
d3+
d3+
3-
d1
m21
m1-1
m12
3+
d3-
1
dm21
dm1-1
dm12
d3-
d3-
d1
3+
m12
m21
m1-1
3-
1
d3+
dm12
dm21
dm1-1
dm1-1
dm1-1
m12
m21
1
d3+
d3-
m1-1
dm12
dm21
d1
3+
3-
dm12
dm12
m21
m1-1
d3-
1
d3+
m12
dm21
dm1-1
3-
d1
3+
dm21
dm21
m1-1
m12
d3+
d3-
1
m21
dm1-1
dm12
3+
3-
d1

Table of projective phases in group multiplication


1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
1
1
1
1
1
1
1
1
1
1
1
1
1
3+
1
1
1
1
1
1
1
1
1
1
1
1
3-
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
m12
1
1
1
1
1
1
1
1
1
1
1
1
m21
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
d3+
1
1
1
1
1
1
1
1
1
1
1
1
d3-
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
dm12
1
1
1
1
1
1
1
1
1
1
1
1
dm21
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 symbolA1A2E1E2EE1
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
1
1
1
(
 1 0
 0 1
)
1
1
(
 1 0
 0 1
)
2
(
  0 -1
  1 -1
)
(
  eiπ/3  0
  0 e-iπ/3
)
3+
1
1
(
 e-2iπ/3  0
  0  e2iπ/3
)
-1
-1
(
  eiπ/3  0
  0 e-iπ/3
)
3
(
 -1  1
 -1  0
)
(
 e-iπ/3  0
  0  eiπ/3
)
3-
1
1
(
  e2iπ/3  0
  0 e-2iπ/3
)
-1
-1
(
 e-iπ/3  0
  0  eiπ/3
)
4
(
 0 1
 1 0
)
(
  0 e5iπ/6
  eiπ/6  0
)
m1-1
1
-1
(
 0 1
 1 0
)
i
-i
(
  0 -1
  1  0
)
5
(
  1 -1
  0 -1
)
(
  0 -i
 -i  0
)
m12
1
-1
(
  0  e2iπ/3
 e-2iπ/3  0
)
i
-i
(
  0  e-iπ/3
 e-2iπ/3  0
)
6
(
 -1  0
 -1  1
)
(
  0  eiπ/6
 e5iπ/6  0
)
m21
1
-1
(
  0 e-2iπ/3
  e2iπ/3  0
)
i
-i
(
  0  eiπ/3
 e2iπ/3  0
)
7
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
d1
1
1
(
 1 0
 0 1
)
-1
-1
(
 -1  0
  0 -1
)
8
(
  0 -1
  1 -1
)
(
 e-2iπ/3  0
  0  e2iπ/3
)
d3+
1
1
(
 e-2iπ/3  0
  0  e2iπ/3
)
1
1
(
 e-2iπ/3  0
  0  e2iπ/3
)
9
(
 -1  1
 -1  0
)
(
  e2iπ/3  0
  0 e-2iπ/3
)
d3-
1
1
(
  e2iπ/3  0
  0 e-2iπ/3
)
1
1
(
  e2iπ/3  0
  0 e-2iπ/3
)
10
(
 0 1
 1 0
)
(
  0  e-iπ/6
 e-5iπ/6  0
)
dm1-1
1
-1
(
 0 1
 1 0
)
-i
i
(
  0  1
 -1  0
)
11
(
  1 -1
  0 -1
)
(
 0 i
 i 0
)
dm12
1
-1
(
  0  e2iπ/3
 e-2iπ/3  0
)
-i
i
(
  0 e2iπ/3
  eiπ/3  0
)
12
(
 -1  0
 -1  1
)
(
  0 e-5iπ/6
  e-iπ/6  0
)
dm21
1
-1
(
  0 e-2iπ/3
  e2iπ/3  0
)
-i
i
(
  0 e-2iπ/3
  e-iπ/3  0
)
k-Subgroupsmag
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