Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{-}\text{4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:25.115.1.1 )

General Positions

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 ‖ m100 | 0 }
a, -b, c | x, y, z	{ 1 ‖ m010 | 0 }
b, a, -c | -x, -y, -z	{ -1 ‖ 2110 | 0 }
-b, -a, -c | -x, -y, -z	{ -1 ‖ 21-10 | 0 }
b, -a, -c | -x, -y, -z	{ -1 ‖ -4+001 | 0 }
-b, a, -c | -x, -y, -z	{ -1 ‖ -4-001 | 0 }
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 ‖ m100 | 0 }
a, -b, c | -x, y, z	{ m ‖ m010 | 0 }
b, a, -c | x, -y, -z	{ 2 ‖ 2110 | 0 }
-b, -a, -c | x, -y, -z	{ 2 ‖ 21-10 | 0 }
b, -a, -c | x, -y, -z	{ 2 ‖ -4+001 | 0 }
-b, a, -c | x, -y, -z	{ 2 ‖ -4-001 | 0 }

Wyckoff Positions

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

Spin Brillouin Zone & k-little co-groups

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

Spin Brillouin Zone

4/mmmP

Band Representations (Magnon)

2e

k-vector	k-vector-G↑	A1↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_1^S(2)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_1^S(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_1^S(1)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_1^S(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$(S)W_1^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$(\Sigma )V_1^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$2(T)E_1^S(1)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(1)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_1^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_1^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$2(Y)C_1^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$2(B)K_1^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$4(D)V_1^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$4(F)N_1^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

2f

k-vector	k-vector-G↑	A1↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_2^S(2)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_2^S(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_3^S(1)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_3^S(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$(S)W_1^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$(\Sigma )V_1^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$2(T)E_2^S(1)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(1)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_2^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_3^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$2(Y)C_2^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$2(B)K_1^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$4(D)V_1^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$4(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

2g

k-vector	k-vector-G↑	A1↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_3^S(2)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_3^S(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_3^S(1)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_3^S(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$(S)W_1^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$(\Sigma )V_1^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$2(T)E_2^S(1)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(1)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_3^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_3^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$2(Y)C_2^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$2(B)K_1^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$4(D)V_1^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$4(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

4j

k-vector	k-vector-G↑	A'↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_4^S(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_1^S(2)\oplus (A)R_4^S(2)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_1^S(2)\oplus (M)S_4^S(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_1^S(1)\oplus 2(R)T_4^S(1)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_1^S(1)\oplus 2(X)Y_4^S(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_4^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_4^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$2(S)W_1^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$2(\Sigma )V_1^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$4(T)E_1^S(1)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(1)\oplus 2(U)B_2^S(1)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_1^S(2)\oplus (V)Q_4^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_1^S(1)\oplus 2(W)H_4^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$4(Y)C_1^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$2(B)K_1^S(1)\oplus 2(B)K_2^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$2(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$4(D)V_1^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$4(F)N_1^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

4k

k-vector	k-vector-G↑	A'↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_4^S(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_2^S(2)\oplus (A)R_3^S(2)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_2^S(2)\oplus (M)S_3^S(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_2^S(1)\oplus 2(R)T_3^S(1)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_2^S(1)\oplus 2(X)Y_3^S(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_4^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_4^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$2(S)W_1^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$2(\Sigma )V_1^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$4(T)E_2^S(1)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(1)\oplus 2(U)B_2^S(1)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_2^S(2)\oplus (V)Q_3^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_2^S(1)\oplus 2(W)H_3^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$4(Y)C_2^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$2(B)K_1^S(1)\oplus 2(B)K_2^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$2(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$4(D)V_1^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$4(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

8l

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)\oplus {\Gamma }_3^S(2)\oplus {\Gamma }_4^S(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_1^S(2)\oplus (A)R_2^S(2)\oplus (A)R_3^S(2)\oplus (A)R_4^S(2)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_1^S(2)\oplus (M)S_2^S(2)\oplus (M)S_3^S(2)\oplus (M)S_4^S(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_1^S(1)\oplus 2(R)T_2^S(1)\oplus 2(R)T_3^S(1)\oplus 2(R)T_4^S(1)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_1^S(1)\oplus 2(X)Y_2^S(1)\oplus 2(X)Y_3^S(1)\oplus 2(X)Y_4^S(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_2^S(2)\oplus Z_3^S(2)\oplus Z_4^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$4(S)W_1^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$4(\Sigma )V_1^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$4(T)E_1^S(1)\oplus 4(T)E_2^S(1)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$4(U)B_1^S(1)\oplus 4(U)B_2^S(1)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_1^S(2)\oplus (V)Q_2^S(2)\oplus (V)Q_3^S(2)\oplus (V)Q_4^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_1^S(1)\oplus 2(W)H_2^S(1)\oplus 2(W)H_3^S(1)\oplus 2(W)H_4^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$4(Y)C_1^S(1)\oplus 4(Y)C_2^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$4(B)K_1^S(1)\oplus 4(B)K_2^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$4(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$8(D)V_1^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$8(E)W_1^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$4(F)N_1^S(1)\oplus 4(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(1)$	Spin Splitting