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Irreducible corepresentations of the Projective Magnetic Point Group 3


Table of characters of the unitary symmetry operations


1
3+
3-
d1
d3+
d3-
A
1
1
1
1
1
1
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
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-
1
1
3+
3-
d1
d3+
d3-
3+
3+
d3-
1
d3+
3-
d1
3-
3-
1
d3+
d3-
d1
3+
d1
d1
d3+
d3-
1
3+
3-
d3+
d3+
3-
d1
3+
d3-
1
d3-
d3-
d1
3+
3-
1
d3+

Table of projective phases in group multiplication


1
3+
3-
d1
d3+
d3-
1
1
1
1
1
1
1
3+
1
1
1
1
1
1
3-
1
1
1
1
1
1
d1
1
1
1
1
1
1
d3+
1
1
1
1
1
1
d3-
1
1
1
1
1
1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolA2E1E1E2EE
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+
1
e2iπ/3
e-2iπ/3
e-iπ/3
eiπ/3
-1
3
(
-1 1
-1 0
)
(
e-iπ/3 0
0 eiπ/3
)
3-
1
e-2iπ/3
e2iπ/3
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+
1
e2iπ/3
e-2iπ/3
e2iπ/3
e-2iπ/3
1
6
(
-1 1
-1 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
d3-
1
e-2iπ/3
e2iπ/3
e-2iπ/3
e2iπ/3
1
k-Subgroupsmag
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