Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}{4}_2/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:49.132.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
a, -b, -c+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 | x, y, z	{ 1 ‖ 2001 | 0 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
-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, 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 | -x, -y, -z	{ -1 ‖ 2110 | 0 }
-b, -a, -c | -x, -y, -z	{ -1 ‖ 21-10 | 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 | -x, -y, -z	{ -1 ‖ m110 | 0 }
b, a, c | -x, -y, -z	{ -1 ‖ m1-10 | 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
a, -b, -c+1/2 | -x, y, z	{ m ‖ 2100 | 0 0 1/2 }
-a, b, -c+1/2 | -x, y, z	{ m ‖ 2010 | 0 0 1/2 }
-a, -b, c | -x, y, z	{ m ‖ 2001 | 0 }
-a, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
-a, b, c+1/2 | -x, y, z	{ m ‖ m100 | 0 0 1/2 }
a, -b, c+1/2 | -x, y, z	{ m ‖ m010 | 0 0 1/2 }
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 | x, -y, -z	{ 2 ‖ 2110 | 0 }
-b, -a, -c | x, -y, -z	{ 2 ‖ 21-10 | 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 | x, -y, -z	{ 2 ‖ m110 | 0 }
b, a, c | x, -y, -z	{ 2 ‖ m1-10 | 0 }

Wyckoff Positions

WP	Site symmetry	Representative
2a	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,0)
2b	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,1/4 | 0,0,0)
2c	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,0 | 0,0,0)
2d	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,1/4 | 0,0,0)
4e	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,1/4 | 0,0,z)
4f	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,0 | 0,0,z)
4g	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,c | 0,0,0)
4h	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,c | 0,0,0)
4i	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,0 | 0,0,0)
4j	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,1/2 | 0,0,0)
8k	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,c | 0,0,z)
8l	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,1/4 | 0,0,z)
8m	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/2,1/4 | 0,0,z)
8n	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,0 | 0,0,z)
8o	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,c | 0,0,0)
16p	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(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)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
M:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Z:(0,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
R:(0,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
X:(0,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
V:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
S:(u,u,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
T:(u,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
U:(0,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
W:(0,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Y:(u,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(0,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,u,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
D:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
E:(u,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
F:(u,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
GP:(u,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$

Spin Brillouin Zone

4/mmmP

Band Representations (Magnon)

4e

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_2^S(4)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_4^{S,+}(2)\oplus (M)S_4^{S,-}(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_2^S(2)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_4^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(4)$
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)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$(S)W_1^S(2)\oplus (S)W_2^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$(\Sigma )V_1^S(2)\oplus (\Sigma )V_2^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$2(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(2)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_3^S(2)\oplus (V)Q_4^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_3^S(1)\oplus 2(W)H_4^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$2(Y)C_3^S(1)\oplus 2(Y)C_4^S(1)$	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)	$2(D)V_1^S(1)\oplus 2(D)V_2^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$2(E)W_1^S(1)\oplus 2(E)W_2^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$2(F)N_1^S(1)\oplus 2(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

4f

k-vector	k-vector-G↑	Ag↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_2^S(4)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_3^{S,-}(2)\oplus (M)S_4^{S,-}(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_2^S(2)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_3^{S,-}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_4^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$(S)W_1^S(2)\oplus (S)W_2^S(2)$
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)	$2(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$2(U)B_1^S(2)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$(V)Q_3^S(2)\oplus (V)Q_4^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$2(W)H_3^S(1)\oplus 2(W)H_4^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$2(Y)C_3^S(1)\oplus 2(Y)C_4^S(1)$	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)	$2(E)W_1^S(1)\oplus 2(E)W_2^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$2(F)N_1^S(1)\oplus 2(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

8k

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$2(A)R_2^S(4)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_3^{S,+}(2)\oplus (M)S_3^{S,-}(2)\oplus (M)S_4^{S,+}(2)\oplus (M)S_4^{S,-}(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$4(R)T_2^S(2)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_3^{S,+}(1)\oplus 2(X)Y_3^{S,-}(1)\oplus 2(X)Y_4^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$2Z_1^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)\oplus 2{\Delta }_3^S(1)\oplus 2{\Delta }_4^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$2(S)W_1^S(2)\oplus 2(S)W_2^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$2(\Sigma )V_1^S(2)\oplus 2(\Sigma )V_2^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$4(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$4(U)B_1^S(2)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$2(V)Q_3^S(2)\oplus 2(V)Q_4^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$4(W)H_3^S(1)\oplus 4(W)H_4^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$2(Y)C_1^S(1)\oplus 2(Y)C_2^S(1)\oplus 2(Y)C_3^S(1)\oplus 2(Y)C_4^S(1)$	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)	$4(D)V_1^S(1)\oplus 4(D)V_2^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)\oplus 4(E)W_2^S(1)$	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

8l

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_1^S(4)\oplus (A)R_2^S(4)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_1^{S,+}(2)\oplus (M)S_1^{S,-}(2)\oplus (M)S_3^{S,+}(2)\oplus (M)S_3^{S,-}(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_1^S(2)\oplus 2(R)T_2^S(2)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_1^{S,-}(1)\oplus 2(X)Y_3^{S,+}(1)\oplus 2(X)Y_3^{S,-}(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(4)\oplus Z_2^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)\oplus 2{\Delta }_3^S(1)\oplus 2{\Delta }_4^S(1)$	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)	$2(S)W_1^S(2)\oplus 2(S)W_2^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$2(\Sigma )V_1^S(2)\oplus 2(\Sigma )V_2^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$4(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$4(U)B_1^S(2)$	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)	$4(D)V_1^S(1)\oplus 4(D)V_2^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)\oplus 4(E)W_2^S(1)$	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

8m

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$(A)R_1^S(4)\oplus (A)R_2^S(4)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_2^{S,+}(2)\oplus (M)S_2^{S,-}(2)\oplus (M)S_4^{S,+}(2)\oplus (M)S_4^{S,-}(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$2(R)T_1^S(2)\oplus 2(R)T_2^S(2)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_2^{S,+}(1)\oplus 2(X)Y_2^{S,-}(1)\oplus 2(X)Y_4^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(4)\oplus Z_2^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)\oplus 2{\Delta }_3^S(1)\oplus 2{\Delta }_4^S(1)$	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)	$2(S)W_1^S(2)\oplus 2(S)W_2^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$2(\Sigma )V_1^S(2)\oplus 2(\Sigma )V_2^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$4(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$4(U)B_1^S(2)$	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)	$4(Y)C_3^S(1)\oplus 4(Y)C_4^S(1)$	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)	$4(D)V_1^S(1)\oplus 4(D)V_2^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)\oplus 4(E)W_2^S(1)$	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

8n

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)	$(A)R_1^S(4)\oplus (A)R_2^S(4)$
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)	$2(R)T_1^S(2)\oplus 2(R)T_2^S(2)$	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)	$Z_1^S(4)\oplus Z_2^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_4^S(1)$	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)	$2(S)W_1^S(2)\oplus 2(S)W_2^S(2)$
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)	$4(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$4(U)B_1^S(2)$	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)	$4(Y)C_1^S(1)\oplus 4(Y)C_4^S(1)$	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)	$4(D)V_1^S(1)\oplus 4(D)V_2^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$4(E)W_1^S(1)\oplus 4(E)W_2^S(1)$	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

16p

k-vector	k-vector-G↑	A↑G(16)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)\oplus {\Gamma }_4^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
A:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$2(A)R_1^S(4)\oplus 2(A)R_2^S(4)$
M:(1/2,1/2,0)	S:(1/2,1/2,0)	$(M)S_1^{S,+}(2)\oplus (M)S_1^{S,-}(2)\oplus (M)S_2^{S,+}(2)\oplus (M)S_2^{S,-}(2)\oplus (M)S_3^{S,+}(2)\oplus (M)S_3^{S,-}(2)\oplus (M)S_4^{S,+}(2)\oplus (M)S_4^{S,-}(2)$
R:(0,1/2,1/2)	T:(0,1/2,1/2)	$4(R)T_1^S(2)\oplus 4(R)T_2^S(2)$	Spin Splitting
X:(0,1/2,0)	Y:(0,1/2,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_1^{S,-}(1)\oplus 2(X)Y_2^{S,+}(1)\oplus 2(X)Y_2^{S,-}(1)\oplus 2(X)Y_3^{S,+}(1)\oplus 2(X)Y_3^{S,-}(1)\oplus 2(X)Y_4^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Z:(0,0,1/2)	Z:(0,0,1/2)	$2Z_1^S(4)\oplus 2Z_2^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)\oplus 4{\Delta }_3^S(1)\oplus 4{\Delta }_4^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 2{\Lambda }_3^S(2)\oplus 2{\Lambda }_4^S(2)$
S:(u,u,1/2)	W:(u,u,1/2)	$4(S)W_1^S(2)\oplus 4(S)W_2^S(2)$
Σ:(u,u,0)	V:(u,u,0)	$4(\Sigma )V_1^S(2)\oplus 4(\Sigma )V_2^S(2)$
T:(u,1/2,1/2)	E:(u,1/2,1/2)	$8(T)E_1^S(2)$	Spin Splitting
U:(0,v,1/2)	B:(0,v,1/2)	$8(U)B_1^S(2)$	Spin Splitting
V:(1/2,1/2,w)	Q:(1/2,1/2,w)	$2(V)Q_1^S(2)\oplus 2(V)Q_2^S(2)\oplus 2(V)Q_3^S(2)\oplus 2(V)Q_4^S(2)$
W:(0,1/2,w)	H:(0,1/2,w)	$4(W)H_1^S(1)\oplus 4(W)H_2^S(1)\oplus 4(W)H_3^S(1)\oplus 4(W)H_4^S(1)$	Spin Splitting
Y:(u,1/2,0)	C:(u,1/2,0)	$4(Y)C_1^S(1)\oplus 4(Y)C_2^S(1)\oplus 4(Y)C_3^S(1)\oplus 4(Y)C_4^S(1)$	Spin Splitting
B:(0,v,w)	K:(0,v,w)	$8(B)K_1^S(1)\oplus 8(B)K_2^S(1)$	Spin Splitting
C:(u,u,w)	GP:(u,u,w)	$8(C)G{P}_1^S(2)$
D:(u,v,0)	V:(u,v,0)	$8(D)V_1^S(1)\oplus 8(D)V_2^S(1)$	Spin Splitting
E:(u,v,1/2)	W:(u,v,1/2)	$8(E)W_1^S(1)\oplus 8(E)W_2^S(1)$	Spin Splitting
F:(u,1/2,w)	N:(u,1/2,w)	$8(F)N_1^S(1)\oplus 8(F)N_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$16G{P}_1^S(1)$	Spin Splitting