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Irreducible representations of the Double Point Group 2/m (No. 5)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
GM1-
Au
GM1-
1
1
1
1
-1
-1
-1
-1
GM2+
Bg
GM2+
1
-1
1
-1
1
-1
1
-1
GM2-
Bu
GM2-
1
-1
1
-1
-1
1
-1
1
GM4+
2Eg
GM3
1
-i
-1
i
1
-i
-1
i
GM3+
1Eg
GM4
1
i
-1
-i
1
i
-1
-i
GM4-
2Eu
GM5
1
-i
-1
i
-1
i
1
-i
GM3-
1Eu
GM6
1
i
-1
-i
-1
-i
1
i
(1): Notation of the irreps according to Koster GF, Dimmok JO, Wheeler RG and Statz H, (1963) Properties of the thirty-two point groups, M.I.T. Press, Cambridge, Mass.
(2): Notation of the irreps according to Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): Notation of the irreps according to C. J. Bradley, A. P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon Press, Oxford, 1972) for the GM point.

Lists of symmetry operations in the conjugacy classes

C1: 1
C2: 2010
C3d1
C4d2010
C5: -1
C6: m010
C7d-1
C8dm010

List of pairs of conjugated irreducible representations

(*GM3,*GM4)
(*GM5,*GM6)
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)
GM1-(1)
GM2+(1)
GM2-(1)
GM3(0)
GM4(0)
GM5(0)
GM6(0)
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
1
1
1
1
1
1
2
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
1
-1
-1
-i
i
-i
i
3
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
1
1
-1
1
-1
1
1
-1
-1
4
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m010
1
-1
-1
1
-i
i
i
-i
5
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
-1
-1
-1
-1
6
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
1
-1
-1
i
-i
i
-i
7
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
d1
1
-1
1
-1
-1
-1
1
1
8
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm010
1
-1
-1
1
i
-i
-i
i
k-Subgroupsmag
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