| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{001}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{001}\right\} \\ \text{A}_1 & \text{BDI} & 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}& -1 & \sqrt[4]{-1} & (-1)^{3/4} & -\mathrm{i} \\ \text{A}_2 & \text{BDI} & 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}& 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}\\ \text{A}_3 & \text{AI} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} & -1 & -(-1)^{3/4} & -\sqrt[4]{-1} &\mathrm{i}\\ \text{A}_4 & \text{AI} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} \\ \text{A}_5 & \text{AI} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} & -1 & (-1)^{3/4} & \sqrt[4]{-1} &\mathrm{i}\\ \text{A}_6 & \text{AI} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} \\ \text{A}_7 & \text{BDI} & 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}& -1 & -\sqrt[4]{-1} & -(-1)^{3/4} & -\mathrm{i} \\ \text{A}_8 & \text{BDI} & 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}& 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}\\ \end{array} \right)\) |
| B | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{\bar{1}\right\} & \left\{m_{001}\right\} \\ \text{B}_1 & \text{BDI} & 1 & -\mathrm{i} & -1 &\mathrm{i}\\ \text{B}_2 & \text{BDI} & 1 & -\mathrm{i} & 1 & -\mathrm{i} \\ \text{B}_3 & \text{BDI} & 1 &\mathrm{i}& -1 & -\mathrm{i} \\ \text{B}_4 & \text{BDI} & 1 &\mathrm{i}& 1 &\mathrm{i}\\ \end{array} \right)\) |
| C | \(\left(0,0,1\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{001}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{001}\right\} \\ \text{C}_1 & \text{BDI} & 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}& -1 & \sqrt[4]{-1} & (-1)^{3/4} & -\mathrm{i} \\ \text{C}_2 & \text{BDI} & 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}& 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}\\ \text{C}_3 & \text{AI} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} & -1 & -(-1)^{3/4} & -\sqrt[4]{-1} &\mathrm{i}\\ \text{C}_4 & \text{AI} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} \\ \text{C}_5 & \text{AI} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} & -1 & (-1)^{3/4} & \sqrt[4]{-1} &\mathrm{i}\\ \text{C}_6 & \text{AI} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} \\ \text{C}_7 & \text{BDI} & 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}& -1 & -\sqrt[4]{-1} & -(-1)^{3/4} & -\mathrm{i} \\ \text{C}_8 & \text{BDI} & 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}& 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}\\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} \\ \text{D}_1 & \text{AIII} & 1 & -\mathrm{i} & (-1)^{3/4} & \sqrt[4]{-1} \\ \text{D}_2 & \text{AIII} & 1 & -\mathrm{i} & -(-1)^{3/4} & -\sqrt[4]{-1} \\ \text{D}_3 & \text{D} & 1 &\mathrm{i}& -\sqrt[4]{-1} & -(-1)^{3/4} \\ \text{D}_4 & \text{D} & 1 &\mathrm{i}& \sqrt[4]{-1} & (-1)^{3/4} \\ \end{array} \right)\) |
| E | \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{\bar{1}\right\} \\ \text{E}_1 & \text{D} & 1 & -1 \\ \text{E}_2 & \text{D} & 1 & 1 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(0,0,t\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{001}\right\} \\ a_1 & \text{BDI} & 1 & -\sqrt[4]{-1} & -(-1)^{3/4} &\mathrm{i}\\ a_2 & \text{AI} & 1 & (-1)^{3/4} & \sqrt[4]{-1} & -\mathrm{i} \\ a_3 & \text{AI} & 1 & -(-1)^{3/4} & -\sqrt[4]{-1} & -\mathrm{i} \\ a_4 & \text{BDI} & 1 & \sqrt[4]{-1} & (-1)^{3/4} &\mathrm{i}\\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} \\ b_1 & \text{BDI} & 1 & -\mathrm{i} \\ b_2 & \text{BDI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},\frac{t}{2},1-\frac{t}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ c_1 & \text{BDI} & 1 \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001}\right\} \\ d_1 & \text{BDI} & 1 & -\mathrm{i} \\ d_2 & \text{BDI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{t}{2},1-\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001}\right\} \\ e_1 & \text{BDI} & 1 & -\mathrm{i} \\ e_2 & \text{BDI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ f_1 & \text{DIII} & 1 \\ \end{array} \right)\) |
| \(g\) | \(\left(0,t,0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001}\right\} \\ g_1 & \text{BDI} & 1 & -\mathrm{i} \\ g_2 & \text{BDI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(h\) | \(\left(0,\frac{t}{2},1-\frac{t}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ h_1 & \text{BDI} & 1 \\ \end{array} \right)\) |