MSG 68.511 \(B_{3g}\)

\(D^0\) EAZ & character of irrep
A \(\left(0,0,0\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{A}_1 & \text{A} & 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1 \\ \text{A}_2 & \text{A} & 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\ \text{A}_3 & \text{A} & 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\ \text{A}_4 & \text{A} & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \text{A}_5 & \text{A} & 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\ \text{A}_6 & \text{A} & 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\ \text{A}_7 & \text{A} & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\ \text{A}_8 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \end{array} \right)\)
B \(\left(1,0,0\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{B}_1 & \text{A} & 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\ \text{B}_2 & \text{A} & 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1 \\ \text{B}_3 & \text{A} & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \text{B}_4 & \text{A} & 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\ \text{B}_5 & \text{A} & 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\ \text{B}_6 & \text{A} & 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\ \text{B}_7 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{B}_8 & \text{A} & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\ \end{array} \right)\)
C \(\left(\frac{1}{2},\frac{1}{2},0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{C}_1 & \text{D} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
D \(\left(0,0,\frac{1}{2}\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{D}_1 & \text{A} & 2 & 0 & 0 & -2 & 0 & 0 & 0 & 0 \\ \text{D}_2 & \text{A} & 2 & 0 & 0 & 2 & 0 & 0 & 0 & 0 \\ \end{array} \right)\)
E \(\left(1,0,\frac{1}{2}\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{E}_1 & \text{A} & 2 & 0 & 0 & -2 & 0 & 0 & 0 & 0 \\ \text{E}_2 & \text{A} & 2 & 0 & 0 & 2 & 0 & 0 & 0 & 0 \\ \end{array} \right)\)
F \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{F}_1 & \text{D} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(D^1\) EAZ & character of irrep
\(a\) \(\left(t,0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ a_1 & \text{A} & 1 & -1 & -e^{-\mathrm{i} \pi t} & e^{-\mathrm{i} \pi t} \\ a_2 & \text{A} & 1 & -1 & e^{-\mathrm{i} \pi t} & -e^{-\mathrm{i} \pi t} \\ a_3 & \text{A} & 1 & 1 & -e^{-\mathrm{i} \pi t} & -e^{-\mathrm{i} \pi t} \\ a_4 & \text{A} & 1 & 1 & e^{-\mathrm{i} \pi t} & e^{-\mathrm{i} \pi t} \\ \end{array} \right)\)
\(b\) \(\left(0,t,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ b_1 & \text{A} & 1 & -1 & -1 & 1 \\ b_2 & \text{A} & 1 & -1 & 1 & -1 \\ b_3 & \text{A} & 1 & 1 & -1 & -1 \\ b_4 & \text{A} & 1 & 1 & 1 & 1 \\ \end{array} \right)\)
\(c\) \(\left(\frac{t}{2},1-\frac{t}{2},0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ c_1 & \text{A} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ c_2 & \text{A} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(d\) \(\left(t,0,\frac{1}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ d_1 & \text{C} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(e\) \(\left(0,t,\frac{1}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ e_1 & \text{D} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(f\) \(\left(\frac{t}{2},1-\frac{t}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{\frac{1}{2},0,0\right\}\right\} \\ f_1 & \text{A} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ f_2 & \text{A} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(g\) \(\left(0,0,\frac{t}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ g_1 & \text{A} & 1 & -1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_2 & \text{A} & 1 & -1 & e^{-\frac{1}{2}\mathrm{i}\pi t} & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_3 & \text{A} & 1 & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_4 & \text{A} & 1 & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(h\) \(\left(1,0,\frac{t}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ h_1 & \text{A} & 1 & -1 & e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi (t+2)} \\ h_2 & \text{A} & 1 & -1 & e^{-\frac{1}{2}\mathrm{i}\pi (t+2)} & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ h_3 & \text{A} & 1 & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ h_4 & \text{A} & 1 & 1 & e^{-\frac{1}{2}\mathrm{i}\pi (t+2)} & e^{-\frac{1}{2}\mathrm{i}\pi (t+2)} \\ \end{array} \right)\)
\(i\) \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ i_1 & \text{D} & 1 & -1 \\ i_2 & \text{D} & 1 & 1 \\ \end{array} \right)\)