| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{101},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{10-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ \text{A}_1 & \text{AI} & 2 & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \text{A}_2 & \text{AI} & 2 & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \text{A}_3 & \text{BDI} & 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 \\ \end{array} \right)\) |
| B | \(\left(\frac{1}{2},0,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{2_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{B}_1 & \text{AIII} & 2 & -\sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{B}_2 & \text{AIII} & 2 & \sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{C}_1 & \text{AI} & 2 & \sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{C}_2 & \text{AI} & 2 & -\sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{101},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{\text{10-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ \text{D}_1 & \text{AIII} & 2 & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \text{D}_2 & \text{AIII} & 2 & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \text{D}_3 & \text{DIII} & 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(\frac{t}{2},0,0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{100}\right\} \\ a_1 & \text{A} & 1 & -\sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & -(-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}\\ a_2 & \text{A} & 1 & (-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} & \sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} \\ a_3 & \text{A} & 1 & -(-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} \\ a_4 & \text{A} & 1 & \sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & (-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}\\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010}\right\} \\ b_1 & \text{C} & 1 & -\mathrm{i} \\ b_2 & \text{C} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ c_1 & \text{AIII} & 1 & -\mathrm{i} e^{-\mathrm{i} \pi t} \\ c_2 & \text{AIII} & 1 &\mathrm{i}e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{001}\right\} \\ d_1 & \text{A} & 1 & \sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & -(-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} \\ d_2 & \text{A} & 1 & -(-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} & \sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}\\ d_3 & \text{A} & 1 & (-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}\\ d_4 & \text{A} & 1 & -\sqrt[4]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & (-1)^{3/4} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} \\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{t}{2},\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} \\ e_1 & \text{DIII} & 1 & -1 & 1 \\ e_2 & \text{D} & 1 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ e_3 & \text{D} & 1 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{1}{2},\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ f_1 & \text{AII} & 1 &\mathrm{i}e^{-\mathrm{i} \pi t} \\ f_2 & \text{AII} & 1 & -\mathrm{i} e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |