Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group -4' (N. 10.3.34)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
GM1
A
GM1
1
1
1
1
GM2GM2
BB
GM2GM2
2
-2
2
-2
GM4GM3
1E2E
GM3GM4
2
0
-2
0
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
C3: d1
C4: d2001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM2GM3GM4
1
(
 1 0 0
 0 1 0
 0 0 1
)
(
 1 0
 0 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  0
  0 -1
)
(
 -i  0
  0  i
)
3
(
 1 0 0
 0 1 0
 0 0 1
)
(
 -1  0
  0 -1
)
d1
1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
4
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
  i  0
  0 -i
)
d2001
1
(
 -1  0
  0 -1
)
(
  i  0
  0 -i
)
5
(
  0  1  0
 -1  0  0
  0  0 -1
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
4'+001
1
(
  0 -1
  1  0
)
(
 0 i
 1 0
)
6
(
  0 -1  0
  1  0  0
  0  0 -1
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
4'-001
1
(
  0  1
 -1  0
)
(
  0 -1
 -i  0
)
7
(
  0  1  0
 -1  0  0
  0  0 -1
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
d4'+001
1
(
  0 -1
  1  0
)
(
  0 -i
 -1  0
)
8
(
  0 -1  0
  1  0  0
  0  0 -1
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
d4'-001
1
(
  0  1
 -1  0
)
(
 0 1
 i 0
)
k-Subgroupsmag
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