Spin Space Group Information

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c \| x, y, z	{ 1 ‖ 1 \| 0 }
a, -b, -c \| x, y, z	{ 1 ‖ 2₁₀₀ \| 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
-a, b, c \| x, y, z	{ 1 ‖ m₁₀₀ \| 0 }
-a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₁₀ \| 1/2 0 1/2 }
-a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₀₁ \| 1/2 0 1/2 }
a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₀₁ \| 1/2 0 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
a, -b, -c \| -x, y, z	{ m ‖ 2₁₀₀ \| 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
-a, b, c \| -x, y, z	{ m ‖ m₁₀₀ \| 0 }
-a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 0 1/2 }
-a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₀₁ \| 1/2 0 1/2 }
a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ m₀₀₁ \| 1/2 0 1/2 }

WP	Site symmetry	Representative
2a	$_{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(0,0,0 \| 0,0,z)
2b	$_{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(1/2,0,0 \| 0,0,z)
2c	$_{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(1/2,1/2,0 \| 0,0,z)
2d	$_{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(0,1/2,0 \| 0,0,z)
4e	$_{}^{}_{}^{1} 2 . ._{}^{}_{}^{\infty m} 1$	(a,0,0 \| 0,0,z)
4f	$_{}^{}_{}^{1} 2 . ._{}^{}_{}^{\infty m} 1$	(a,1/2,0 \| 0,0,z)
4g	$._{}^{}_{}^{- 1} 2 ._{}^{}_{}^{\infty m} 1$	(1/4,b,1/4 \| 0,0,0)
4h	$_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(0,b,c \| 0,0,z)
8i	$_{}^{}_{}^{1} 1_{}^{}_{}^{\infty m} 1$	(a,b,c \| 0,0,z)

Wavevector-k	Little co-group
Γ:(0,0,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
R:(1/2,1/2,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
S:(1/2,1/2,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
T:(0,1/2,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
U:(1/2,0,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
X:(1/2,0,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
Y:(0,1/2,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
Z:(0,0,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty m} 1$
A:(u,0,1/2)	$_{}^{}_{}^{m} m_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
B:(0,v,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
C:(u,1/2,0)	$_{}^{}_{}^{m} m_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
D:(1/2,v,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
Δ:(0,v,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
E:(u,1/2,1/2)	$_{}^{}_{}^{m} m_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
G:(1/2,0,w)	$_{}^{}_{}^{1} m_{}^{}_{}^{2} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty} 1$
H:(0,1/2,w)	$_{}^{}_{}^{1} m_{}^{}_{}^{2} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty} 1$
Λ:(0,0,w)	$_{}^{}_{}^{1} m_{}^{}_{}^{2} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty} 1$
P:(1/2,v,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
Q:(1/2,1/2,w)	$_{}^{}_{}^{1} m_{}^{}_{}^{2} m_{}^{}_{}^{- 1} m_{}^{}_{}^{\infty} 1$
Σ:(u,0,0)	$_{}^{}_{}^{m} m_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
K:(0,v,w)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
L:(1/2,v,w)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
M:(u,0,w)	$_{}^{}_{}^{- 1} 2/_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
N:(u,1/2,w)	$_{}^{}_{}^{- 1} 2/_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
V:(u,v,0)	$_{}^{}_{}^{- 1} 2/_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
W:(u,v,1/2)	$_{}^{}_{}^{- 1} 2/_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
GP:(u,v,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty} 1$

Spin Brillouin Zone

k-vector	k-vector-G↑	Ag↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{1}^{S, +} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{1}^{S, +} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{1}^{S, +} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, +} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{1}^{S, +} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$(A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$(B) G_{1}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$(C) F_{1}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$(D) F_{1}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$(Δ) F_{1}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$(E) G_{1}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$(G) W_{1}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$(H) V_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$(P) G_{1}^{S} G_{2}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$(Q) U_{1}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$2 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$2 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$(M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$(N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$(V) F_{1}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$(W) G_{1}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$2 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	Ag↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{1}^{S, -} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{1}^{S, +} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{1}^{S, -} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, -} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{1}^{S, +} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, -} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$(A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$(B) G_{2}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$(C) F_{1}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$(D) F_{1}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$(Δ) F_{1}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$(E) G_{2}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$(G) W_{1}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$(H) V_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$(P) G_{2}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$(Q) U_{1}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$2 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$2 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$(M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$(N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$(V) F_{1}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$(W) G_{2}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$2 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	Ag↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{2}^{S, +} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{2}^{S, -} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{2}^{S, +} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, -} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, -} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$(A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$(B) G_{2}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$(C) F_{1}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$(D) F_{1}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$(Δ) F_{1}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$(E) G_{2}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$(G) W_{1}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$(H) V_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$(P) G_{2}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$(Q) U_{2}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$2 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$2 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$(M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$(N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$(V) F_{1}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$(W) G_{2}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$2 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	Ag↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{2}^{S, -} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{2}^{S, -} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{2}^{S, -} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, +} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$(A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$(B) G_{1}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$(C) F_{1}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$(D) F_{1}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$(Δ) F_{1}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$(E) G_{1}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$(G) W_{1}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$(H) V_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$(P) G_{1}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$(Q) U_{2}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$2 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$2 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$(M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$(N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$(V) F_{1}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$(W) G_{1}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$2 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{1}^{S, -} (2) \oplus (R) E_{1}^{S, +} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{1}^{S, +} (2) \oplus (S) A_{1}^{S, -} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{1}^{S, -} (2) \oplus (T) D_{1}^{S, +} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, -} (2) \oplus (U) C_{1}^{S, +} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2) \oplus (X) Y_{1}^{S, -} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{1}^{S, +} (2) \oplus (Y) B_{1}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, -} (2) \oplus Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$(A) G_{1}^{S} (2) \oplus (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$(B) G_{1}^{S} (2) \oplus (B) G_{2}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$(C) F_{1}^{S} (2) \oplus (C) F_{2}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$(D) F_{1}^{S} (2) \oplus (D) F_{2}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$(Δ) F_{1}^{S} (2) \oplus (Δ) F_{2}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$(E) G_{1}^{S} (2) \oplus (E) G_{2}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$2 (G) W_{1}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$2 (H) V_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$(P) G_{1}^{S} (2) \oplus (P) G_{2}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$2 (Q) U_{1}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$(Σ) F_{1}^{S} (2) \oplus (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$4 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$4 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$2 (M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$2 (N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$(V) F_{1}^{S} (2) \oplus (V) F_{2}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$(W) G_{1}^{S} (2) \oplus (W) G_{2}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$4 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{2}^{S, -} (2) \oplus (R) E_{2}^{S, +} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{2}^{S, +} (2) \oplus (S) A_{2}^{S, -} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{2}^{S, -} (2) \oplus (T) D_{2}^{S, +} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, -} (2) \oplus (U) C_{1}^{S, +} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2) \oplus (X) Y_{1}^{S, -} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{2}^{S, +} (2) \oplus (Y) B_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, -} (2) \oplus Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$(A) G_{1}^{S} (2) \oplus (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$(B) G_{1}^{S} (2) \oplus (B) G_{2}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$(C) F_{1}^{S} (2) \oplus (C) F_{2}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$(D) F_{1}^{S} (2) \oplus (D) F_{2}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$(Δ) F_{1}^{S} (2) \oplus (Δ) F_{2}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$(E) G_{1}^{S} (2) \oplus (E) G_{2}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$2 (G) W_{1}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$2 (H) V_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$(P) G_{1}^{S} (2) \oplus (P) G_{2}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$2 (Q) U_{2}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$(Σ) F_{1}^{S} (2) \oplus (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$4 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$4 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$2 (M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$2 (N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$(V) F_{1}^{S} (2) \oplus (V) F_{2}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$(W) G_{1}^{S} (2) \oplus (W) G_{2}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$4 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	A'↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{2}^{S, -} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{1}^{S, +} (2) \oplus (R) E_{2}^{S, -} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{1}^{S, +} (2) \oplus (S) A_{2}^{S, -} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{1}^{S, +} (2) \oplus (T) D_{2}^{S, -} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, +} (2) \oplus (U) C_{2}^{S, -} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2) \oplus (X) Y_{2}^{S, -} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{1}^{S, +} (2) \oplus (Y) B_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2) \oplus Z_{2}^{S, -} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$2 (A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$2 (B) G_{1}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$2 (C) F_{1}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$2 (D) F_{1}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$2 (Δ) F_{1}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$2 (E) G_{1}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$(G) W_{1}^{S} (2) \oplus (G) W_{2}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$(H) V_{1}^{S} (2) \oplus (H) V_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2) \oplus Λ_{2}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$2 (P) G_{1}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$(Q) U_{1}^{S} (2) \oplus (Q) U_{2}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$2 (Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$4 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$4 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$2 (M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$2 (N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$2 (V) F_{1}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$2 (W) G_{1}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$4 G P_{1}^{S} (1)$	Spin Splitting

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2) \oplus Γ_{2}^{S, +} (2) \oplus Γ_{2}^{S, -} (2)$
R:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(R) E_{1}^{S, +} (2) \oplus (R) E_{1}^{S, -} (2) \oplus (R) E_{2}^{S, +} (2) \oplus (R) E_{2}^{S, -} (2)$
S:(1/2,1/2,0)	A:(1/2,0,1/2)	$(S) A_{1}^{S, +} (2) \oplus (S) A_{1}^{S, -} (2) \oplus (S) A_{2}^{S, +} (2) \oplus (S) A_{2}^{S, -} (2)$
T:(0,1/2,-1/2)	D:(0,1/2,1/2)	$(T) D_{1}^{S, +} (2) \oplus (T) D_{1}^{S, -} (2) \oplus (T) D_{2}^{S, +} (2) \oplus (T) D_{2}^{S, -} (2)$
U:(1/2,0,-1/2)	C:(1/2,1/2,0)	$(U) C_{1}^{S, +} (2) \oplus (U) C_{1}^{S, -} (2) \oplus (U) C_{2}^{S, +} (2) \oplus (U) C_{2}^{S, -} (2)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X) Y_{1}^{S, +} (2) \oplus (X) Y_{1}^{S, -} (2) \oplus (X) Y_{2}^{S, +} (2) \oplus (X) Y_{2}^{S, -} (2)$
Y:(0,1/2,0)	B:(0,0,1/2)	$(Y) B_{1}^{S, +} (2) \oplus (Y) B_{1}^{S, -} (2) \oplus (Y) B_{2}^{S, +} (2) \oplus (Y) B_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2) \oplus Z_{2}^{S, +} (2) \oplus Z_{2}^{S, -} (2)$
A:(u,0,-1/2)	G:(u,1/2,0)	$2 (A) G_{1}^{S} (2) \oplus 2 (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(0,1/2,v)	$2 (B) G_{1}^{S} (2) \oplus 2 (B) G_{2}^{S} (2)$
C:(u,1/2,0)	F:(u,0,1/2)	$2 (C) F_{1}^{S} (2) \oplus 2 (C) F_{2}^{S} (2)$
D:(1/2,v,0)	F:(1/2,0,v)	$2 (D) F_{1}^{S} (2) \oplus 2 (D) F_{2}^{S} (2)$
Δ:(0,v,0)	F:(0,0,v)	$2 (Δ) F_{1}^{S} (2) \oplus 2 (Δ) F_{2}^{S} (2)$
E:(u,1/2,-1/2)	G:(u,1/2,1/2)	$2 (E) G_{1}^{S} (2) \oplus 2 (E) G_{2}^{S} (2)$
G:(1/2,0,w)	W:(1/2,-w,0)	$2 (G) W_{1}^{S} (2) \oplus 2 (G) W_{2}^{S} (2)$
H:(0,1/2,w)	V:(0,-w,1/2)	$2 (H) V_{1}^{S} (2) \oplus 2 (H) V_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{2}^{S} (2)$
P:(1/2,v,-1/2)	G:(1/2,1/2,v)	$2 (P) G_{1}^{S} (2) \oplus 2 (P) G_{2}^{S} (2)$
Q:(1/2,1/2,w)	U:(1/2,-w,1/2)	$2 (Q) U_{1}^{S} (2) \oplus 2 (Q) U_{2}^{S} (2)$
Σ:(u,0,0)	F:(u,0,0)	$2 (Σ) F_{1}^{S} (2) \oplus 2 (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(0,-w,v)	$8 (K) G P_{1}^{S} (1)$	Spin Splitting
L:(1/2,v,w)	GP:(1/2,-w,v)	$8 (L) G P_{1}^{S} (1)$	Spin Splitting
M:(u,0,w)	GP:(u,-w,0)	$4 (M) G P_{1}^{S} (2)$
N:(u,1/2,w)	GP:(u,-w,1/2)	$4 (N) G P_{1}^{S} (2)$
V:(u,v,0)	F:(u,0,v)	$2 (V) F_{1}^{S} (2) \oplus 2 (V) F_{2}^{S} (2)$
W:(u,v,-1/2)	G:(u,1/2,v)	$2 (W) G_{1}^{S} (2) \oplus 2 (W) G_{2}^{S} (2)$
GP:(u,v,w)	GP:(u,-w,v)	$8 G P_{1}^{S} (1)$	Spin Splitting

Coordinates	Seitz symbol
a, b, c \| x, y, z	{ 1 ‖ 1 \| 0 }
a, -b, -c \| x, y, z	{ 1 ‖ 2₁₀₀ \| 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
-a, b, c \| x, y, z	{ 1 ‖ m₁₀₀ \| 0 }
-a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₁₀ \| 1/2 0 1/2 }
-a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₀₁ \| 1/2 0 1/2 }
a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₀₁ \| 1/2 0 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
a, -b, -c \| -x, y, z	{ m ‖ 2₁₀₀ \| 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
-a, b, c \| -x, y, z	{ m ‖ m₁₀₀ \| 0 }
-a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 0 1/2 }
-a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₀₁ \| 1/2 0 1/2 }
a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ m₀₀₁ \| 1/2 0 1/2 }

Information of spin space group PA1A221mA-1A22-1nA-1A22-1aA∞mA22∞m1 ( nSSG:10.53.1.1 )

Information of spin space group $P_{}^{}_{}^{1} m_{}^{}_{}^{- 1} n_{}^{}_{}^{- 1} a_{}^{}_{}^{\infty m} 1$ ( nSSG:10.53.1.1 )