MSG 142.565 \(A_u\)

\(D^0\) EAZ & character of irrep
A \(\left(0,0,0\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{A}_1 & \text{AI} & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 \\ \text{A}_2 & \text{AI} & 2 & 0 & 0 & 0 & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
B \(\left(\frac{1}{2},\frac{1}{2},0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{B}_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
C \(\left(0,0,1\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{C}_1 & \text{AIII} & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 \\ \text{C}_2 & \text{AIII} & 2 & 0 & 0 & 0 & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
D \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{D}_1 & \text{CI} & 1 & 1 &\mathrm{i}& -\mathrm{i} \\ \text{D}_2 & \text{C} & 1 & 1 & -\mathrm{i} &\mathrm{i}\\ \text{D}_3 & \text{C} & 1 & -1 &\mathrm{i}&\mathrm{i}\\ \text{D}_4 & \text{CI} & 1 & -1 & -\mathrm{i} & -\mathrm{i} \\ \end{array} \right)\)
E \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{E}_1 & \text{C} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(D^1\) EAZ & character of irrep
\(a\) \(\left(0,0,t\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} \\ a_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(b\) \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ b_1 & \text{CI} & 1 &\mathrm{i}\\ b_2 & \text{CI} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(c\) \(\left(\frac{t}{2},\frac{t}{2},1-\frac{t}{2}\right)\) \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ c_1 & \text{CI} & 1 \\ \end{array} \right)\)
\(d\) \(\left(\frac{t}{2},\frac{t}{2},0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ d_1 & \text{CI} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ d_2 & \text{CI} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(e\) \(\left(\frac{t}{2},1-\frac{t}{2},0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ e_1 & \text{C} & 1 &\mathrm{i}e^{\frac{i \pi t}{2}} \\ e_2 & \text{C} & 1 & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ \end{array} \right)\)
\(f\) \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ f_1 & \text{C} & 1 & e^{\frac{i \pi t}{2}} \\ f_2 & \text{C} & 1 & -e^{\frac{i \pi t}{2}} \\ \end{array} \right)\)
\(g\) \(\left(0,t,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ g_1 & \text{C} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(h\) \(\left(0,\frac{t}{2},1-\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} \\ h_1 & \text{C} & 1 &\mathrm{i}e^{\frac{i \pi t}{2}} \\ h_2 & \text{C} & 1 & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ \end{array} \right)\)