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

WP	Site symmetry	Representative
4a	$_{}^{}_{}^{- 1} 2_{}^{}_{}^{- 1} 2_{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(0,0,1/4 \| 0,0,0)
4b	$_{}^{}_{}^{- 1} 2_{}^{}_{}^{- 1} 2_{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(0,1/2,1/4 \| 0,0,0)
4c	$. ._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(0,0,0 \| 0,0,z)
4d	$. ._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(0,1/2,0 \| 0,0,z)
4e	$. ._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(1/4,1/4,0 \| 0,0,z)
4f	$. ._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(1/4,3/4,0 \| 0,0,z)
8g	$_{}^{}_{}^{- 1} 2 . ._{}^{}_{}^{\infty m} 1$	(a,0,1/4 \| 0,0,0)
8h	$._{}^{}_{}^{- 1} 2 ._{}^{}_{}^{\infty m} 1$	(0,b,1/4 \| 0,0,0)
8i	$. ._{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(0,0,c \| 0,0,z)
8j	$. ._{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(0,1/2,c \| 0,0,z)
8k	$. ._{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(1/4,1/4,c \| 0,0,z)
8l	$. ._{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(a,b,0 \| 0,0,z)
16m	$_{}^{}_{}^{1} 1_{}^{}_{}^{\infty m} 1$	(a,b,c \| 0,0,z)

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

Spin Brillouin Zone

mmmC

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)	C:(1/2,1/2,0)	$2 (R) C_{1}^{S, +} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{1}^{S, +} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{1}^{S, +} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{1}^{S, +} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u/2,1/2,-u/2)	$(A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{1}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$2 (D) W_{1}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$(H) U_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$(K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$(M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{1}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$2 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{2}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{1}^{S, +} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{1}^{S, +} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u/2,1/2,-u/2)	$(A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{1}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$2 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$(H) U_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$(K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$(M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{1}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$2 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{2}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{2}^{S, -} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, +} (2)$
A:(u,0,-1/2)	G:(u/2,1/2,-u/2)	$(A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{1}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$2 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$(H) U_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$(K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$(M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{1}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$2 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{2}^{S, +} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{2}^{S, +} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{2}^{S, -} (2)$
Z:(0,0,-1/2)	Z:(0,1/2,0)	$Z_{1}^{S, -} (2)$
A:(u,0,-1/2)	G:(u/2,1/2,-u/2)	$(A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{2}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$2 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$(H) U_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$(K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$(M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{2}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$2 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{1}^{S, +} (1) \oplus 2 (R) C_{1}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{1}^{S, +} (1) \oplus 2 (S) Y_{1}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{1}^{S, +} (2) \oplus (T) E_{1}^{S, -} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{1}^{S, +} (2) \oplus (Y) A_{1}^{S, -} (2)$
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/2,1/2,-u/2)	$(A) G_{1}^{S} (2) \oplus (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{1}^{S} (2) \oplus (B) G_{2}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$4 (D) W_{1}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2) \oplus (Δ) F_{2}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$2 (H) U_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2) \oplus (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$2 (K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$2 (M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1) \oplus 2 (P) F_{2}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{1}^{S} (1) \oplus 2 (Q) G_{2}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$4 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{2}^{S, +} (1) \oplus 2 (R) C_{2}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{2}^{S, +} (1) \oplus 2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{1}^{S, +} (2) \oplus (T) E_{1}^{S, -} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{1}^{S, +} (2) \oplus (Y) A_{1}^{S, -} (2)$
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/2,1/2,-u/2)	$(A) G_{1}^{S} (2) \oplus (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{1}^{S} (2) \oplus (B) G_{2}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$4 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2) \oplus (Δ) F_{2}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$2 (H) U_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2) \oplus (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$2 (K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$2 (M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1) \oplus 2 (P) F_{2}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{1}^{S} (1) \oplus 2 (Q) G_{2}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$4 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{2}^{S, +} (1) \oplus 2 (R) C_{2}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{2}^{S, +} (1) \oplus 2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{2}^{S, +} (2) \oplus (T) E_{2}^{S, -} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{2}^{S, +} (2) \oplus (Y) A_{2}^{S, -} (2)$
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/2,1/2,-u/2)	$(A) G_{1}^{S} (2) \oplus (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$(B) G_{1}^{S} (2) \oplus (B) G_{2}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$4 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$(Δ) F_{1}^{S} (2) \oplus (Δ) F_{2}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$2 (H) U_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$(Σ) F_{1}^{S} (2) \oplus (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$2 (K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$2 (M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$2 (P) F_{1}^{S} (1) \oplus 2 (P) F_{2}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$2 (Q) G_{1}^{S} (1) \oplus 2 (Q) G_{2}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$4 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{1}^{S, +} (1) \oplus 2 (R) C_{2}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{1}^{S, +} (1) \oplus 2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{1}^{S, +} (2) \oplus (T) E_{2}^{S, -} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{1}^{S, +} (2) \oplus (Y) A_{2}^{S, -} (2)$
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/2,1/2,-u/2)	$2 (A) G_{1}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$2 (B) G_{1}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$2 (D) W_{1}^{S} (1) \oplus 2 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$2 (Δ) F_{1}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$(H) U_{2}^{S} (2) \oplus (H) U_{1}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$Λ_{1}^{S} (2) \oplus Λ_{2}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$2 (Σ) F_{1}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$2 (K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$2 (M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$4 (P) F_{1}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$4 (Q) G_{1}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$4 G P_{1}^{S} (1)$	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)	C:(1/2,1/2,0)	$2 (R) C_{1}^{S, +} (1) \oplus 2 (R) C_{1}^{S, -} (1) \oplus 2 (R) C_{2}^{S, +} (1) \oplus 2 (R) C_{2}^{S, -} (1)$	Spin Splitting
S:(1/2,1/2,0)	Y:(1/2,0,0)	$2 (S) Y_{1}^{S, +} (1) \oplus 2 (S) Y_{1}^{S, -} (1) \oplus 2 (S) Y_{2}^{S, +} (1) \oplus 2 (S) Y_{2}^{S, -} (1)$	Spin Splitting
T:(0,1,-1/2)	E:(1/2,1/2,1/2)	$(T) E_{1}^{S, +} (2) \oplus (T) E_{1}^{S, -} (2) \oplus (T) E_{2}^{S, +} (2) \oplus (T) E_{2}^{S, -} (2)$
Y:(0,1,0)	A:(1/2,0,1/2)	$(Y) A_{1}^{S, +} (2) \oplus (Y) A_{1}^{S, -} (2) \oplus (Y) A_{2}^{S, +} (2) \oplus (Y) A_{2}^{S, -} (2)$
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/2,1/2,-u/2)	$2 (A) G_{1}^{S} (2) \oplus 4 (A) G_{2}^{S} (2)$
B:(0,v,-1/2)	G:(v/2,1/2,v/2)	$2 (B) G_{1}^{S} (2) \oplus 2 (B) G_{2}^{S} (2)$
D:(1/2,1/2,w)	W:(1/2,-w,0)	$4 (D) W_{1}^{S} (1) \oplus 4 (D) W_{2}^{S} (1)$	Spin Splitting
Δ:(0,v,0)	F:(v/2,0,v/2)	$2 (Δ) F_{1}^{S} (2) \oplus 2 (Δ) F_{2}^{S} (2)$
H:(0,1,w)	U:(1/2,-w,1/2)	$2 (H) U_{1}^{S} (2) \oplus 2 (H) U_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,-w,0)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{2}^{S} (2)$
Σ:(u,0,0)	F:(u/2,0,-u/2)	$2 (Σ) F_{1}^{S} (2) \oplus 2 (Σ) F_{2}^{S} (2)$
K:(0,v,w)	GP:(v/2,-w,v/2)	$4 (K) G P_{1}^{S} (2)$
M:(u,0,w)	GP:(u/2,-w,-u/2)	$4 (M) G P_{1}^{S} (2)$
P:(u,v,0)	F:(u/2+v/2,0,-u/2+v/2)	$4 (P) F_{1}^{S} (1) \oplus 4 (P) F_{2}^{S} (1)$	Spin Splitting
Q:(u,v,-1/2)	G:(u/2+v/2,1/2,-u/2+v/2)	$4 (Q) G_{1}^{S} (1) \oplus 4 (Q) G_{2}^{S} (1)$	Spin Splitting
GP:(u,v,w)	GP:(u/2+v/2,-w,-u/2+v/2)	$8 G P_{1}^{S} (1)$	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 }
a, -b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 0 0 1/2 }
-a, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₁₀ \| 0 0 1/2 }
-a, b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 0 0 1/2 }
a, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 0 0 1/2 }
a+1/2, b+1/2, c \| x, y, z	{ 1 ‖ 1 \| 1/2 1/2 0 }
-a+1/2, -b+1/2, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 1/2 1/2 0 }
-a+1/2, -b+1/2, -c \| x, y, z	{ 1 ‖ -1 \| 1/2 1/2 0 }
a+1/2, b+1/2, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 1/2 1/2 0 }
a+1/2, -b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 1/2 1/2 1/2 }
-a+1/2, b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₁₀ \| 1/2 1/2 1/2 }
-a+1/2, b+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 1/2 1/2 1/2 }
a+1/2, -b+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 1/2 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 }
a, -b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 0 0 1/2 }
-a, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 0 0 1/2 }
-a, b, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 0 0 1/2 }
a, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 0 0 1/2 }
a+1/2, b+1/2, c \| -x, y, z	{ m ‖ 1 \| 1/2 1/2 0 }
-a+1/2, -b+1/2, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 1/2 1/2 0 }
-a+1/2, -b+1/2, -c \| -x, y, z	{ m ‖ -1 \| 1/2 1/2 0 }
a+1/2, b+1/2, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 1/2 1/2 0 }
a+1/2, -b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 1/2 1/2 1/2 }
-a+1/2, b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 1/2 1/2 }
-a+1/2, b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 1/2 1/2 1/2 }
a+1/2, -b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 1/2 1/2 }

Information of spin space group CA-1A22-1cA-1A22-1cA1A221mA∞mA22∞m1 ( nSSG:10.66.1.1 )

Information of spin space group $C_{}^{}_{}^{- 1} c_{}^{}_{}^{- 1} c_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$ ( nSSG:10.66.1.1 )