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Irreducible corepresentations of the Projective Magnetic Point Group 3m'


Table of characters of the unitary symmetry operations


1
3+
3-
d1
d3+
d3-
2E
1
e2iπ/3
e-2iπ/3
1
e2iπ/3
e-2iπ/3
1E
1
e-2iπ/3
e2iπ/3
1
e-2iπ/3
e2iπ/3
A
1
1
1
1
1
1
1E
1
e-iπ/3
eiπ/3
-1
e2iπ/3
e-2iπ/3
2E
1
eiπ/3
e-iπ/3
-1
e-2iπ/3
e2iπ/3
E
1
-1
-1
-1
1
1

Multiplication table of the symmetry operations


1
3+
3-
d1
d3+
d3-
m'1-1
m'12
m'21
dm'1-1
dm'12
dm'21
1
1
3+
3-
d1
d3+
d3-
m'1-1
m'12
m'21
dm'1-1
dm'12
dm'21
3+
3+
d3-
1
d3+
3-
d1
dm'21
dm'1-1
dm'12
m'21
m'1-1
m'12
3-
3-
1
d3+
d3-
d1
3+
dm'12
dm'21
dm'1-1
m'12
m'21
m'1-1
d1
d1
d3+
d3-
1
3+
3-
dm'1-1
dm'12
dm'21
m'1-1
m'12
m'21
d3+
d3+
3-
d1
3+
d3-
1
m'21
m'1-1
m'12
dm'21
dm'1-1
dm'12
d3-
d3-
d1
3+
3-
1
d3+
m'12
m'21
m'1-1
dm'12
dm'21
dm'1-1
m'1-1
m'1-1
dm'12
dm'21
dm'1-1
m'12
m'21
1
d3+
d3-
d1
3+
3-
m'12
m'12
dm'21
dm'1-1
dm'12
m'21
m'1-1
d3-
1
d3+
3-
d1
3+
m'21
m'21
dm'1-1
dm'12
dm'21
m'1-1
m'12
d3+
d3-
1
3+
3-
d1
dm'1-1
dm'1-1
m'12
m'21
m'1-1
dm'12
dm'21
d1
3+
3-
1
d3+
d3-
dm'12
dm'12
m'21
m'1-1
m'12
dm'21
dm'1-1
3-
d1
3+
d3-
1
d3+
dm'21
dm'21
m'1-1
m'12
m'21
dm'1-1
dm'12
3+
3-
d1
d3+
d3-
1

Table of projective phases in group multiplication


1
3+
3-
d1
d3+
d3-
m'1-1
m'12
m'21
dm'1-1
dm'12
dm'21
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
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
m'1-1
1
1
1
1
1
1
1
1
1
1
1
1
m'12
1
1
1
1
1
1
1
1
1
1
1
1
m'21
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
dm'12
1
1
1
1
1
1
1
1
1
1
1
1
dm'21
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 symbol2E1EA1E2EE
1
(
1 0
0 1
)
(
1 0
0 1
)
1
1
1
1
1
1
1
2
(
0 -1
1 -1
)
(
eiπ/3 0
0 e-iπ/3
)
3+
e2iπ/3
e-2iπ/3
1
e-iπ/3
eiπ/3
-1
3
(
-1 1
-1 0
)
(
e-iπ/3 0
0 eiπ/3
)
3-
e-2iπ/3
e2iπ/3
1
eiπ/3
e-iπ/3
-1
4
(
1 0
0 1
)
(
-1 0
0 -1
)
d1
1
1
1
-1
-1
-1
5
(
0 -1
1 -1
)
(
e-2iπ/3 0
0 e2iπ/3
)
d3+
e2iπ/3
e-2iπ/3
1
e2iπ/3
e-2iπ/3
1
6
(
-1 1
-1 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
d3-
e-2iπ/3
e2iπ/3
1
e-2iπ/3
e2iπ/3
1
7
(
0 1
1 0
)
(
0 e5iπ/6
eiπ/6 0
)
m'1-1
-1
-1
-1
-1
-1
-1
8
(
1 -1
0 -1
)
(
0 -i
-i 0
)
m'12
e-iπ/3
eiπ/3
-1
e-iπ/3
eiπ/3
-1
9
(
-1 0
-1 1
)
(
0 eiπ/6
e5iπ/6 0
)
m'21
eiπ/3
e-iπ/3
-1
eiπ/3
e-iπ/3
-1
10
(
0 1
1 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
dm'1-1
-1
-1
-1
1
1
1
11
(
1 -1
0 -1
)
(
0 i
i 0
)
dm'12
e-iπ/3
eiπ/3
-1
e2iπ/3
e-2iπ/3
1
12
(
-1 0
-1 1
)
(
0 e-5iπ/6
e-iπ/6 0
)
dm'21
eiπ/3
e-iπ/3
-1
e-2iπ/3
e2iπ/3
1
k-Subgroupsmag
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