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Irreducible corepresentations of the Projective Magnetic Point Group 34π/31'


Table of characters of the unitary symmetry operations


1
3+
3-
d1
d3+
d3-
1E
1
e-2iπ/3
e2iπ/3
1
e-2iπ/3
e2iπ/3
2EA
2
eiπ/3
e-iπ/3
2
eiπ/3
e-iπ/3
2E2E
2
2eiπ/3
2e-iπ/3
-2
2e-2iπ/3
2e2iπ/3
1EE
2
e-2iπ/3
e2iπ/3
-2
eiπ/3
e-iπ/3

Multiplication table of the symmetry operations


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

Table of projective phases in group multiplication


1
3+
3-
d1
d3+
d3-
1'
3+'
3-'
d1'
d3+'
d3-'
1
1
1
1
1
1
1
1
1
1
1
1
1
3+
1
1
1
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
3-
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
d1
1
1
1
1
1
1
1
1
1
1
1
1
d3+
1
1
1
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
d3-
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
1'
1
1
1
1
1
1
1
1
1
1
1
1
3+'
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
3-'
1
1
1
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
d1'
1
1
1
1
1
1
1
1
1
1
1
1
d3+'
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
d3-'
1
1
1
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbol1E2EA2E2E1EE
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
1
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
2
(
  0 -1
  1 -1
)
(
  eiπ/3  0
  0 e-iπ/3
)
3+
e-2iπ/3
(
  1  0
  0 e2iπ/3
)
(
 eiπ/3  0
  0 eiπ/3
)
(
  -1  0
  0 e-iπ/3
)
3
(
 -1  1
 -1  0
)
(
 e-iπ/3  0
  0  eiπ/3
)
3-
e2iπ/3
(
  1  0
  0 e-2iπ/3
)
(
 e-iπ/3  0
  0 e-iπ/3
)
(
  -1  0
  0 eiπ/3
)
4
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
d1
1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
5
(
  0 -1
  1 -1
)
(
 e-2iπ/3  0
  0  e2iπ/3
)
d3+
e-2iπ/3
(
  1  0
  0 e2iπ/3
)
(
 e-2iπ/3  0
  0 e-2iπ/3
)
(
  1  0
  0 e2iπ/3
)
6
(
 -1  1
 -1  0
)
(
  e2iπ/3  0
  0 e-2iπ/3
)
d3-
e2iπ/3
(
  1  0
  0 e-2iπ/3
)
(
 e2iπ/3  0
  0 e2iπ/3
)
(
  1  0
  0 e-2iπ/3
)
7
(
 1 0
 0 1
)
(
 1 0
 0 1
)
1'
-1
(
 0 1
 1 0
)
(
  0  1
 -1  0
)
(
  0 -1
  1  0
)
8
(
  0 -1
  1 -1
)
(
  eiπ/3  0
  0 e-iπ/3
)
3+'
eiπ/3
(
  0 e-2iπ/3
  1  0
)
(
  0  eiπ/3
 e-2iπ/3  0
)
(
  0 e-2iπ/3
  -1  0
)
9
(
 -1  1
 -1  0
)
(
 e-iπ/3  0
  0  eiπ/3
)
3-'
e-iπ/3
(
  0 e2iπ/3
  1  0
)
(
  0 e-iπ/3
 e2iπ/3  0
)
(
  0 e2iπ/3
  -1  0
)
10
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
d1'
-1
(
 0 1
 1 0
)
(
  0 -1
  1  0
)
(
  0  1
 -1  0
)
11
(
  0 -1
  1 -1
)
(
 e-2iπ/3  0
  0  e2iπ/3
)
d3+'
eiπ/3
(
  0 e-2iπ/3
  1  0
)
(
  0 e-2iπ/3
  eiπ/3  0
)
(
  0 eiπ/3
  1  0
)
12
(
 -1  1
 -1  0
)
(
  e2iπ/3  0
  0 e-2iπ/3
)
d3-'
e-iπ/3
(
  0 e2iπ/3
  1  0
)
(
  0 e2iπ/3
 e-iπ/3  0
)
(
  0 e-iπ/3
  1  0
)
k-Subgroupsmag
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