Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 4'm'm (N. 13.3.46)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
GM1
A1
GM1
1
1
1
1
1
GM3
A2
GM2
1
1
-1
-1
1
GM4GM2
B1B2
GM3GM4
2
-2
0
0
2
GM5
E
GM5
2
0
0
0
-2
The notation used in this table is an extension to corepresentations of the following notations used for irreducible representations:
(1): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, based on Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love (1979) Kronecher Product Tables, 1, General Introduction and Tables of Irreducible Representations of Space groups. New York: IFI/Plenum, for the GM point.

Lists of unitary symmetry operations in the conjugacy classes

C1: 1
C2: 2001, d2001
C3: m110, dm110
C4: m110, dm110
C5: d1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM3GM4GM5
1
(
 1 0 0
 0 1 0
 0 0 1
)
(
 1 0
 0 1
)
1
1
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
2
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
 -i  0
  0  i
)
2001
1
1
(
 -1  0
  0 -1
)
(
  0 -1
  1  0
)
3
(
  0 -1  0
 -1  0  0
  0  0  1
)
(
  0 -(1+i)√2/2
  (1-i)√2/2  0
)
m110
1
-1
(
  1  0
  0 -1
)
(
 -i  0
  0  i
)
4
(
 0 1 0
 1 0 0
 0 0 1
)
(
  0 -(1-i)√2/2
  (1+i)√2/2  0
)
m1-10
1
-1
(
 -1  0
  0  1
)
(
  0 -i
 -i  0
)
5
(
 1 0 0
 0 1 0
 0 0 1
)
(
 -1  0
  0 -1
)
d1
1
1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
6
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
  i  0
  0 -i
)
d2001
1
1
(
 -1  0
  0 -1
)
(
  0  1
 -1  0
)
7
(
  0 -1  0
 -1  0  0
  0  0  1
)
(
  0  (1+i)√2/2
 -(1-i)√2/2  0
)
dm110
1
-1
(
  1  0
  0 -1
)
(
  i  0
  0 -i
)
8
(
 0 1 0
 1 0 0
 0 0 1
)
(
  0  (1-i)√2/2
 -(1+i)√2/2  0
)
dm1-10
1
-1
(
 -1  0
  0  1
)
(
 0 i
 i 0
)
9
(
  0 -1  0
  1  0  0
  0  0  1
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
4'+001
1
-1
(
  0 -1
  1  0
)
(
 -1/√2 -1/√2
  1/√2 -1/√2
)
10
(
  0  1  0
 -1  0  0
  0  0  1
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
4'-001
1
-1
(
  0  1
 -1  0
)
(
  1/√2 -1/√2
  1/√2  1/√2
)
11
(
  1  0  0
  0 -1  0
  0  0  1
)
(
  0 -1
  1  0
)
m'010
1
1
(
 0 1
 1 0
)
(
 -i/√2  i/√2
  i/√2  i/√2
)
12
(
 -1  0  0
  0  1  0
  0  0  1
)
(
  0 -i
 -i  0
)
m'100
1
1
(
  0 -1
 -1  0
)
(
  i/√2  i/√2
  i/√2 -i/√2
)
13
(
  0 -1  0
  1  0  0
  0  0  1
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
d4'+001
1
-1
(
  0 -1
  1  0
)
(
  1/√2  1/√2
 -1/√2  1/√2
)
14
(
  0  1  0
 -1  0  0
  0  0  1
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
d4'-001
1
-1
(
  0  1
 -1  0
)
(
 -1/√2  1/√2
 -1/√2 -1/√2
)
15
(
  1  0  0
  0 -1  0
  0  0  1
)
(
  0  1
 -1  0
)
dm'010
1
1
(
 0 1
 1 0
)
(
  i/√2 -i/√2
 -i/√2 -i/√2
)
16
(
 -1  0  0
  0  1  0
  0  0  1
)
(
 0 i
 i 0
)
dm'100
1
1
(
  0 -1
 -1  0
)
(
 -i/√2 -i/√2
 -i/√2  i/√2
)
k-Subgroupsmag
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