Corepresentations PG

Bilbao Crystallographic Server

COREPRESENTATIONS PG

Irreducible corepresentations of the Projective Magnetic Point Group 2_πmm

Table of characters of the unitary symmetry operations

	1	2	m₁₀	m₀₁	^d1	^d2	^dm₁₀	^dm₀₁
AB	2	0	0	0	2	0	0	0

¹E₁	1	i	i	i	-1	-i	-i	-i
²E₁	1	i	-i	-i	-1	-i	i	i
¹E₂	1	-i	i	-i	-1	i	-i	i
²E₂	1	-i	-i	i	-1	i	i	-i

Multiplication table of the symmetry operations

	1	2	m₁₀	m₀₁	^d1	^d2	^dm₁₀	^dm₀₁
1	1	2	m₁₀	m₀₁	^d1	^d2	^dm₁₀	^dm₀₁
2	2	^d1	m₀₁	^dm₁₀	^d2	1	^dm₀₁	m₁₀
m₁₀	m₁₀	^dm₀₁	^d1	2	^dm₁₀	m₀₁	1	^d2
m₀₁	m₀₁	m₁₀	^d2	^d1	^dm₀₁	^dm₁₀	2	1
^d1	^d1	^d2	^dm₁₀	^dm₀₁	1	2	m₁₀	m₀₁
^d2	^d2	1	^dm₀₁	m₁₀	2	^d1	m₀₁	^dm₁₀
^dm₁₀	^dm₁₀	m₀₁	1	^d2	m₁₀	^dm₀₁	^d1	2
^dm₀₁	^dm₀₁	^dm₁₀	2	1	m₀₁	m₁₀	^d2	^d1

Table of projective phases in group multiplication

	1	2	m₁₀	m₀₁	^d1	^d2	^dm₁₀	^dm₀₁
1	1	1	1	1	1	1	1	1
2	1	1	i	-i	1	1	i	-i
m₁₀	1	-i	1	i	1	-i	1	i
m₀₁	1	i	-i	1	1	i	-i	1
^d1	1	1	1	1	1	1	1	1
^d2	1	1	i	-i	1	1	i	-i
^dm₁₀	1	-i	1	i	1	-i	1	i
^dm₀₁	1	i	-i	1	1	i	-i	1

Matrices of the representations of the group

The antiunitary operations are written in red color

N

Matrix presentation

Seitz symbol

AB

¹E₁

²E₁

¹E₂

²E₂

1

 1  0
 0  1

 1  0
 0  1

1

 1  0
 0  1

1

1

1

1

2

 -1   0
  0  -1

 -i   0
  0   i

2

 -1   0
  0   1

i

i

-i

-i

3

 -1   0
  0   1

  0  -i
 -i   0

m₁₀

 0  1
 1  0

i

-i

i

-i

4

  1   0
  0  -1

  0  -1
  1   0

m₀₁

  0   i
 -i   0

i

-i

-i

i

5

 1  0
 0  1

 -1   0
  0  -1

^d1

 1  0
 0  1

-1

-1

-1

-1

6

 -1   0
  0  -1

  i   0
  0  -i

^d2

 -1   0
  0   1

-i

-i

i

i

7

 -1   0
  0   1

 0  i
 i  0

^dm₁₀

 0  1
 1  0

-i

i

-i

i

8

  1   0
  0  -1

  0   1
 -1   0

^dm₀₁

  0   i
 -i   0

-i

i

i

-i

k-Subgroupsmag

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