MSG 70.529

\(D^0\) EAZ & character of irrep
A \(\left(0,0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ \text{A}_1 & \text{AI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
B \(\left(0,1,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ \text{B}_1 & \text{A} & 1 & -\mathrm{i} & -\mathrm{i} & 1 \\ \text{B}_2 & \text{A} & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ \text{B}_3 & \text{A} & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ \text{B}_4 & \text{A} & 1 &\mathrm{i}&\mathrm{i}& 1 \\ \end{array} \right)\)
C \(\left(0,0,1\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ \text{C}_1 & \text{A} & 1 & -\mathrm{i} & -1 & -\mathrm{i} \\ \text{C}_2 & \text{A} & 1 & -\mathrm{i} & 1 &\mathrm{i}\\ \text{C}_3 & \text{A} & 1 &\mathrm{i}& -1 &\mathrm{i}\\ \text{C}_4 & \text{A} & 1 &\mathrm{i}& 1 & -\mathrm{i} \\ \end{array} \right)\)
D \(\left(1,0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ \text{D}_1 & \text{AI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(D^1\) EAZ & character of irrep
\(a\) \(\left(t,0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ a_1 & \text{AI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(b\) \(\left(-t,0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ b_1 & \text{AI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(c\) \(\left(t,0,1\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ c_1 & \text{A} & 1 & -\mathrm{i} & -e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ c_2 & \text{A} & 1 & -\mathrm{i} & e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ c_3 & \text{A} & 1 &\mathrm{i}& -e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ c_4 & \text{A} & 1 &\mathrm{i}& e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(d\) \(\left(-t,0,1\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{3}{4},\frac{3}{4}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ d_1 & \text{A} & 1 & -\mathrm{i} & -e^{\frac{i \pi t}{2}} & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ d_2 & \text{A} & 1 & -\mathrm{i} & e^{\frac{i \pi t}{2}} &\mathrm{i}e^{\frac{i \pi t}{2}} \\ d_3 & \text{A} & 1 &\mathrm{i}& -e^{\frac{i \pi t}{2}} &\mathrm{i}e^{\frac{i \pi t}{2}} \\ d_4 & \text{A} & 1 &\mathrm{i}& e^{\frac{i \pi t}{2}} & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ \end{array} \right)\)
\(e\) \(\left(0,1,t\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{\frac{1}{4},0,\frac{1}{4}\right\}\right\} \\ e_1 & \text{A} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ e_2 & \text{A} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(f\) \(\left(t,1-t,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ f_1 & \text{A} & 1 & -1 \\ f_2 & \text{A} & 1 & 1 \\ \end{array} \right)\)
\(g\) \(\left(-t,1-t,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{\frac{1}{4},\frac{1}{4},0\right\}\right\} \\ g_1 & \text{A} & 1 & -e^{i \pi t} \\ g_2 & \text{A} & 1 & e^{i \pi t} \\ \end{array} \right)\)