\(D^0\) | EAZ & character of irrep | |
A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{A}_1 & \text{AI} & 2 & 0 & 0 & 0 & -\sqrt{2} & \sqrt{2} & 0 & 0 \\ \text{A}_2 & \text{AI} & 2 & 0 & 0 & 0 & \sqrt{2} & -\sqrt{2} & 0 & 0 \\ \end{array} \right)\) |
B | \(\left(0,\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{B}_1 & \text{A} & 1 & -\mathrm{i} & -1 & -\mathrm{i} \\ \text{B}_2 & \text{A} & 1 & -\mathrm{i} & 1 &\mathrm{i}\\ \text{B}_3 & \text{A} & 1 &\mathrm{i}& -1 &\mathrm{i}\\ \text{B}_4 & \text{A} & 1 &\mathrm{i}& 1 & -\mathrm{i} \\ \end{array} \right)\) |
C | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{C}_1 & \text{A} & 2 & 0 & 0 & 0 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 \\ \text{C}_2 & \text{A} & 2 & 0 & 0 & 0 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 \\ \end{array} \right)\) |
D | \(\left(0,0,\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{D}_1 & \text{A} & 2 & 0 & 0 & 0 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 \\ \text{D}_2 & \text{A} & 2 & 0 & 0 & 0 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 \\ \end{array} \right)\) |
E | \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{E}_1 & \text{A} & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ \text{E}_2 & \text{A} & 1 & -\mathrm{i} & -\mathrm{i} & 1 \\ \text{E}_3 & \text{A} & 1 &\mathrm{i}&\mathrm{i}& 1 \\ \text{E}_4 & \text{A} & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ \end{array} \right)\) |
F | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{F}_1 & \text{AII} & 2 & 0 & 0 & 0 & -\sqrt{2} & \sqrt{2} & 0 & 0 \\ \text{F}_2 & \text{AII} & 2 & 0 & 0 & 0 & \sqrt{2} & -\sqrt{2} & 0 & 0 \\ \end{array} \right)\) |
\(D^1\) | EAZ & character of irrep | |
\(a\) | \(\left(0,\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ a_1 & \text{A} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ a_2 & \text{A} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\) |
\(b\) | \(\left(\frac{1-t}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ b_1 & \text{AII} & 1 & e^{\frac{i \pi t}{2}} \\ b_2 & \text{AII} & 1 & -e^{\frac{i \pi t}{2}} \\ \end{array} \right)\) |
\(c\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ c_1 & \text{A} & 1 & -\mathrm{i} e^{-\mathrm{i} \pi t} \\ c_2 & \text{A} & 1 &\mathrm{i}e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |
\(d\) | \(\left(0,\frac{t}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ d_1 & \text{A} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ d_2 & \text{A} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\) |
\(e\) | \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ e_1 & \text{AII} & 1 & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ e_2 & \text{AII} & 1 & e^{\frac{1}{2}\mathrm{i}\pi (t-3)} \\ \end{array} \right)\) |
\(f\) | \(\left(\frac{t}{2},\frac{t}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ f_1 & \text{AII} & 1 &\mathrm{i}e^{-\mathrm{i} \pi t} \\ f_2 & \text{AII} & 1 & -\mathrm{i} e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |
\(g\) | \(\left(0,0,\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ g_1 & \text{AI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
\(h\) | \(\left(0,\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ h_1 & \text{A} & 1 & -\mathrm{i} & -e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi (t+1)} \\ h_2 & \text{A} & 1 & -\mathrm{i} & e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ h_3 & \text{A} & 1 &\mathrm{i}& -e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ h_4 & \text{A} & 1 &\mathrm{i}& e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi (t+1)} \\ \end{array} \right)\) |
\(i\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ i_1 & \text{AII} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
\(j\) | \(\left(0,\frac{1}{2},-\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ j_1 & \text{A} & 1 & -\mathrm{i} & -e^{\frac{i \pi t}{2}} & e^{\frac{1}{2}\mathrm{i}\pi (t-1)} \\ j_2 & \text{A} & 1 & -\mathrm{i} & e^{\frac{i \pi t}{2}} &\mathrm{i}e^{\frac{i \pi t}{2}} \\ j_3 & \text{A} & 1 &\mathrm{i}& -e^{\frac{i \pi t}{2}} &\mathrm{i}e^{\frac{i \pi t}{2}} \\ j_4 & \text{A} & 1 &\mathrm{i}& e^{\frac{i \pi t}{2}} & e^{\frac{1}{2}\mathrm{i}\pi (t-1)} \\ \end{array} \right)\) |