Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}{4}_2/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{n}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:86.86.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

WP	Site symmetry	Representative
2a	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-4}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,1/4,1/4 |0,0,z)
2b	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-4}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,1/4,3/4 |0,0,z)
4c	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 |0,0,z)
4d	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,1/2 |0,0,z)
4e	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(3/4,1/4,c |0,0,z)
4f	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,1/4,c |0,0,z)
8g	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(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)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
M:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Z:(0,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
R:(0,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
X:(0,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
V:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
D:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
E:(u,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
S:(u,u,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
T:(u,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
U:(0,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
W:(0,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Y:(u,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(0,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,u,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
F:(u,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
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

Band Representations (Magnon)

2a

k-vector	A↑G(2)
A:(1/2,1/2,1/2)	$A_1^{S,+}(1)\oplus A_2^{S,-}(1)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_2^{S,-}(1)$
M:(1/2,1/2,0)	$M_1^S(2)$
Z:(0,0,1/2)	$Z_1^S(2)$
R:(0,1/2,1/2)	$R_1^S(2)$
X:(0,1/2,0)	$X_1^S(2)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_2^S(1)$
D:(u,v,0)	$D_1^S(1)\oplus D_2^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)\oplus {\Delta }_2^S(1)$
E:(u,v,1/2)	$E_1^S(1)\oplus E_2^S(1)$
S:(u,u,1/2)	$S_1^S(1)\oplus S_2^S(1)$
Σ:(u,u,0)	${\Sigma }_1^S(1)\oplus {\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$T_1^S(1)\oplus T_2^S(1)$
U:(0,v,1/2)	$U_1^S(1)\oplus U_2^S(1)$
W:(0,1/2,w)	$W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$Y_1^S(1)\oplus Y_2^S(1)$
B:(0,v,w)	$2B_1^S(1)$
C:(u,u,w)	$2C_1^S(1)$
F:(u,1/2,w)	$2F_1^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

2b

k-vector	A↑G(2)
A:(1/2,1/2,1/2)	$A_1^{S,-}(1)\oplus A_2^{S,+}(1)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_2^{S,-}(1)$
M:(1/2,1/2,0)	$M_1^S(2)$
Z:(0,0,1/2)	$Z_1^S(2)$
R:(0,1/2,1/2)	$R_1^S(2)$
X:(0,1/2,0)	$X_1^S(2)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_2^S(1)$
D:(u,v,0)	$D_1^S(1)\oplus D_2^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)\oplus {\Delta }_2^S(1)$
E:(u,v,1/2)	$E_1^S(1)\oplus E_2^S(1)$
S:(u,u,1/2)	$S_1^S(1)\oplus S_2^S(1)$
Σ:(u,u,0)	${\Sigma }_1^S(1)\oplus {\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$T_1^S(1)\oplus T_2^S(1)$
U:(0,v,1/2)	$U_1^S(1)\oplus U_2^S(1)$
W:(0,1/2,w)	$W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$Y_1^S(1)\oplus Y_2^S(1)$
B:(0,v,w)	$2B_1^S(1)$
C:(u,u,w)	$2C_1^S(1)$
F:(u,1/2,w)	$2F_1^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

4c

k-vector	Ag↑G(4)
A:(1/2,1/2,1/2)	$A_1^{S,+}(1)\oplus A_2^{S,+}(1)\oplus A_3^{S,+}{A}_4^{S,+}(2)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_2^{S,+}(1)\oplus {\Gamma }_3^{S,+}{\Gamma }_4^{S,+}(2)$
M:(1/2,1/2,0)	$M_1^S(2)\oplus M_2^S(2)$
Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_2^S(2)$
R:(0,1/2,1/2)	$2R_1^S(2)$
X:(0,1/2,0)	$2X_1^S(2)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus {\Lambda }_3^S{\Lambda }_4^S(2)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_2^S(1)\oplus V_3^S{V}_4^S(2)$
D:(u,v,0)	$2D_1^S(1)\oplus 2D_2^S(1)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
E:(u,v,1/2)	$2E_1^S(1)\oplus 2E_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)\oplus 2S_2^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$2T_1^S(1)\oplus 2T_2^S(1)$
U:(0,v,1/2)	$2U_1^S(1)\oplus 2U_2^S(1)$
W:(0,1/2,w)	$2W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$2Y_1^S(1)\oplus 2Y_2^S(1)$
B:(0,v,w)	$4B_1^S(1)$
C:(u,u,w)	$4C_1^S(1)$
F:(u,1/2,w)	$4F_1^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$

4d

k-vector	Ag↑G(4)
A:(1/2,1/2,1/2)	$A_1^{S,-}(1)\oplus A_2^{S,-}(1)\oplus A_3^{S,-}{A}_4^{S,-}(2)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_2^{S,+}(1)\oplus {\Gamma }_3^{S,+}{\Gamma }_4^{S,+}(2)$
M:(1/2,1/2,0)	$M_1^S(2)\oplus M_2^S(2)$
Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_2^S(2)$
R:(0,1/2,1/2)	$2R_1^S(2)$
X:(0,1/2,0)	$2X_1^S(2)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus {\Lambda }_3^S{\Lambda }_4^S(2)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_2^S(1)\oplus V_3^S{V}_4^S(2)$
D:(u,v,0)	$2D_1^S(1)\oplus 2D_2^S(1)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
E:(u,v,1/2)	$2E_1^S(1)\oplus 2E_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)\oplus 2S_2^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$2T_1^S(1)\oplus 2T_2^S(1)$
U:(0,v,1/2)	$2U_1^S(1)\oplus 2U_2^S(1)$
W:(0,1/2,w)	$2W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$2Y_1^S(1)\oplus 2Y_2^S(1)$
B:(0,v,w)	$4B_1^S(1)$
C:(u,u,w)	$4C_1^S(1)$
F:(u,1/2,w)	$4F_1^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$

4e

k-vector	A↑G(4)
A:(1/2,1/2,1/2)	$A_3^{S,+}{A}_4^{S,+}(2)\oplus A_3^{S,-}{A}_4^{S,-}(2)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_1^{S,-}(1)\oplus {\Gamma }_2^{S,+}(1)\oplus {\Gamma }_2^{S,-}(1)$
M:(1/2,1/2,0)	$2M_2^S(2)$
Z:(0,0,1/2)	$2Z_1^S(2)$
R:(0,1/2,1/2)	$2R_1^S(2)$
X:(0,1/2,0)	$2X_1^S(2)$
Λ:(0,0,w)	$2{\Lambda }_1^S(1)\oplus 2{\Lambda }_2^S(1)$
V:(1/2,1/2,w)	$2V_3^S{V}_4^S(2)$
D:(u,v,0)	$2D_1^S(1)\oplus 2D_2^S(1)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
E:(u,v,1/2)	$2E_1^S(1)\oplus 2E_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)\oplus 2S_2^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$2T_1^S(1)\oplus 2T_2^S(1)$
U:(0,v,1/2)	$2U_1^S(1)\oplus 2U_2^S(1)$
W:(0,1/2,w)	$2W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$2Y_1^S(1)\oplus 2Y_2^S(1)$
B:(0,v,w)	$4B_1^S(1)$
C:(u,u,w)	$4C_1^S(1)$
F:(u,1/2,w)	$4F_1^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$

4f

k-vector	A↑G(4)
A:(1/2,1/2,1/2)	$A_1^{S,+}(1)\oplus A_1^{S,-}(1)\oplus A_2^{S,+}(1)\oplus A_2^{S,-}(1)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_1^{S,-}(1)\oplus {\Gamma }_2^{S,+}(1)\oplus {\Gamma }_2^{S,-}(1)$
M:(1/2,1/2,0)	$2M_1^S(2)$
Z:(0,0,1/2)	$2Z_1^S(2)$
R:(0,1/2,1/2)	$2R_1^S(2)$
X:(0,1/2,0)	$2X_1^S(2)$
Λ:(0,0,w)	$2{\Lambda }_1^S(1)\oplus 2{\Lambda }_2^S(1)$
V:(1/2,1/2,w)	$2V_1^S(1)\oplus 2V_2^S(1)$
D:(u,v,0)	$2D_1^S(1)\oplus 2D_2^S(1)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
E:(u,v,1/2)	$2E_1^S(1)\oplus 2E_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)\oplus 2S_2^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$2T_1^S(1)\oplus 2T_2^S(1)$
U:(0,v,1/2)	$2U_1^S(1)\oplus 2U_2^S(1)$
W:(0,1/2,w)	$2W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$2Y_1^S(1)\oplus 2Y_2^S(1)$
B:(0,v,w)	$4B_1^S(1)$
C:(u,u,w)	$4C_1^S(1)$
F:(u,1/2,w)	$4F_1^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$

8g

k-vector	A↑G(8)
A:(1/2,1/2,1/2)	$A_1^{S,+}(1)\oplus A_1^{S,-}(1)\oplus A_2^{S,+}(1)\oplus A_2^{S,-}(1)\oplus A_3^{S,+}{A}_4^{S,+}(2)\oplus A_3^{S,-}{A}_4^{S,-}(2)$
Γ:(0,0,0)	${\Gamma }_1^{S,+}(1)\oplus {\Gamma }_1^{S,-}(1)\oplus {\Gamma }_2^{S,+}(1)\oplus {\Gamma }_2^{S,-}(1)\oplus {\Gamma }_3^{S,+}{\Gamma }_4^{S,+}(2)\oplus {\Gamma }_3^{S,-}{\Gamma }_4^{S,-}(2)$
M:(1/2,1/2,0)	$2M_1^S(2)\oplus 2M_2^S(2)$
Z:(0,0,1/2)	$2Z_1^S(2)\oplus 2Z_2^S(2)$
R:(0,1/2,1/2)	$4R_1^S(2)$
X:(0,1/2,0)	$4X_1^S(2)$
Λ:(0,0,w)	$2{\Lambda }_1^S(1)\oplus 2{\Lambda }_2^S(1)\oplus 2{\Lambda }_3^S{\Lambda }_4^S(2)$
V:(1/2,1/2,w)	$2V_1^S(1)\oplus 2V_2^S(1)\oplus 2V_3^S{V}_4^S(2)$
D:(u,v,0)	$4D_1^S(1)\oplus 4D_2^S(1)$
Δ:(0,v,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)$
E:(u,v,1/2)	$4E_1^S(1)\oplus 4E_2^S(1)$
S:(u,u,1/2)	$4S_1^S(1)\oplus 4S_2^S(1)$
Σ:(u,u,0)	$4{\Sigma }_1^S(1)\oplus 4{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$4T_1^S(1)\oplus 4T_2^S(1)$
U:(0,v,1/2)	$4U_1^S(1)\oplus 4U_2^S(1)$
W:(0,1/2,w)	$4W_1^S{W}_2^S(2)$
Y:(u,1/2,0)	$4Y_1^S(1)\oplus 4Y_2^S(1)$
B:(0,v,w)	$8B_1^S(1)$
C:(u,u,w)	$8C_1^S(1)$
F:(u,1/2,w)	$8F_1^S(1)$
GP:(u,v,w)	$8G{P}_1^S(1)$