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Irreducible representations of the Double Point Group m (No. 4)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
GM1
A'
GM1
1
1
1
1
GM2
A''
GM2
1
-1
1
-1
GM4
2E
GM3
1
-i
-1
i
GM3
1E
GM4
1
i
-1
-i
(1): Notation of the irreps according to Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Notation of the irreps according to 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): Notation of the irreps according to 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 symmetry operations in the conjugacy classes

C1: 1
C2: m010
C3d1
C4dm010

List of pairs of conjugated irreducible representations

(*GM3,*GM4)
Matrices of the representations of the group

The number in parentheses after the label of the irrep indicates the "reality" of the irrep: (1) for real, (-1) for pseudoreal and (0) for complex representations.

N
Matrix presentation
Seitz Symbol
GM1(1)
GM2(1)
GM3(0)
GM4(0)
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
1
1
2
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m010
1
-1
-i
i
3
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
-1
-1
4
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm010
1
-1
i
-i
k-Subgroupsmag
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