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 ‖ 2₀₀₁ \| 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
a, b, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 0 }
-b, a, c+1/2 \| -x, -y, -z	{ -1 ‖ 4⁺₀₀₁ \| 0 0 1/2 }
b, -a, c+1/2 \| -x, -y, -z	{ -1 ‖ 4^-₀₀₁ \| 0 0 1/2 }
b, -a, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4⁺₀₀₁ \| 0 0 1/2 }
-b, a, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4^-₀₀₁ \| 0 0 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
-a, -b, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
a, b, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 0 }
-b, a, c+1/2 \| x, -y, -z	{ 2 ‖ 4⁺₀₀₁ \| 0 0 1/2 }
b, -a, c+1/2 \| x, -y, -z	{ 2 ‖ 4^-₀₀₁ \| 0 0 1/2 }
b, -a, -c+1/2 \| x, -y, -z	{ 2 ‖ -4⁺₀₀₁ \| 0 0 1/2 }
-b, a, -c+1/2 \| x, -y, -z	{ 2 ‖ -4^-₀₀₁ \| 0 0 1/2 }

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

Wavevector-k	Little co-group
A:(1/2,1/2,1/2)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
Γ:(0,0,0)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
M:(1/2,1/2,0)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
Z:(0,0,1/2)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
R:(0,1/2,1/2)	$_{}^{}_{}^{1} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
X:(0,1/2,0)	$_{}^{}_{}^{1} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
Λ:(0,0,w)	$_{}^{}_{}^{2} 4/_{}^{}_{}^{m} m_{}^{}_{}^{\infty} 1$
V:(1/2,1/2,w)	$_{}^{}_{}^{2} 4/_{}^{}_{}^{m} m_{}^{}_{}^{\infty} 1$
D:(u,v,0)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
Δ:(0,v,0)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
E:(u,v,1/2)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
S:(u,u,1/2)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
Σ:(u,u,0)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
T:(u,1/2,1/2)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
U:(0,v,1/2)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
W:(0,1/2,w)	$_{}^{}_{}^{1} 2/_{}^{}_{}^{m} m_{}^{}_{}^{\infty} 1$
Y:(u,1/2,0)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
B:(0,v,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty} 1$
C:(u,u,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty} 1$
F:(u,1/2,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty} 1$
GP:(u,v,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty} 1$

Spin Brillouin Zone

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

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

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

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

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

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

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

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

k-vector	k-vector-G↑	A↑G(8)
A:(1/2,1/2,-1/2)	E:(1/2,1/2,1/2)	$(A) E_{1}^{S, +} (2) \oplus (A) E_{1}^{S, -} (2) \oplus (A) E_{2}^{S, +} (2) \oplus (A) E_{2}^{S, -} (2)$
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2) \oplus Γ_{2}^{S, +} (2) \oplus Γ_{2}^{S, -} (2)$
M:(1/2,1/2,0)	A:(1/2,0,1/2)	$(M) A_{1}^{S, +} (2) \oplus (M) A_{1}^{S, -} (2) \oplus (M) A_{2}^{S, +} (2) \oplus (M) A_{2}^{S, -} (2)$
R:(0,1/2,-1/2)	D:(0,1/2,1/2)	$2 (R) D_{1}^{S, +} (1) \oplus 2 (R) D_{1}^{S, -} (1) \oplus 2 (R) D_{2}^{S, +} (1) \oplus 2 (R) D_{2}^{S, -} (1)$	Spin Splitting
X:(0,1/2,0)	B:(0,0,1/2)	$2 (X) B_{1}^{S, +} (1) \oplus 2 (X) B_{1}^{S, -} (1) \oplus 2 (X) B_{2}^{S, +} (1) \oplus 2 (X) B_{2}^{S, -} (1)$	Spin Splitting
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2) \oplus Z_{2}^{S, +} (2) \oplus Z_{2}^{S, -} (2)$
B:(0,v,w)	GP:(0,-w,v)	$8 (B) G P_{1}^{S} (1)$	Spin Splitting
C:(u,u,w)	GP:(u,-w,u)	$8 (C) G P_{1}^{S} (1)$	Spin Splitting
D:(u,v,0)	F:(u,0,v)	$4 (D) F_{1}^{S} (1) \oplus 4 (D) F_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(0,0,v)	$4 (Δ) F_{1}^{S} (1) \oplus 4 (Δ) F_{2}^{S} (1)$	Spin Splitting
E:(u,v,-1/2)	G:(u,1/2,v)	$4 (E) G_{1}^{S} (1) \oplus 4 (E) G_{2}^{S} (1)$	Spin Splitting
F:(u,1/2,w)	GP:(u,-w,1/2)	$8 (F) G P_{1}^{S} (1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{2}^{S} (2)$
S:(u,u,-1/2)	G:(u,1/2,u)	$4 (S) G_{1}^{S} (1) \oplus 4 (S) G_{2}^{S} (1)$	Spin Splitting
Σ:(u,u,0)	F:(u,0,u)	$4 (Σ) F_{1}^{S} (1) \oplus 4 (Σ) F_{2}^{S} (1)$	Spin Splitting
T:(u,1/2,-1/2)	G:(u,1/2,1/2)	$4 (T) G_{1}^{S} (1) \oplus 4 (T) G_{2}^{S} (1)$	Spin Splitting
U:(0,v,-1/2)	G:(0,1/2,v)	$4 (U) G_{1}^{S} (1) \oplus 4 (U) G_{2}^{S} (1)$	Spin Splitting
V:(1/2,1/2,w)	U:(1/2,-w,1/2)	$2 (V) U_{1}^{S} (2) \oplus 2 (V) U_{2}^{S} (2)$
W:(0,1/2,w)	V:(0,-w,1/2)	$4 (W) V_{1}^{S} (1) \oplus 4 (W) V_{2}^{S} (1)$	Spin Splitting
Y:(u,1/2,0)	F:(u,0,1/2)	$4 (Y) F_{1}^{S} (1) \oplus 4 (Y) F_{2}^{S} (1)$	Spin Splitting
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 ‖ 2₀₀₁ \| 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
a, b, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 0 }
-b, a, c+1/2 \| -x, -y, -z	{ -1 ‖ 4⁺₀₀₁ \| 0 0 1/2 }
b, -a, c+1/2 \| -x, -y, -z	{ -1 ‖ 4^-₀₀₁ \| 0 0 1/2 }
b, -a, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4⁺₀₀₁ \| 0 0 1/2 }
-b, a, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4^-₀₀₁ \| 0 0 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
-a, -b, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
a, b, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 0 }
-b, a, c+1/2 \| x, -y, -z	{ 2 ‖ 4⁺₀₀₁ \| 0 0 1/2 }
b, -a, c+1/2 \| x, -y, -z	{ 2 ‖ 4^-₀₀₁ \| 0 0 1/2 }
b, -a, -c+1/2 \| x, -y, -z	{ 2 ‖ -4⁺₀₀₁ \| 0 0 1/2 }
-b, a, -c+1/2 \| x, -y, -z	{ 2 ‖ -4^-₀₀₁ \| 0 0 1/2 }

Information of spin space group PA-1A22-142/A1A221mA∞mA22∞m1 ( nSSG:10.84.1.1 )

Information of spin space group $P_{}^{}_{}^{- 1} 4_{2} /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$ ( nSSG:10.84.1.1 )