MSG 201.18 \(A_g\)

\(D^0\) EAZ & character of irrep
A \(\left(0,0,0\right)\) \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{3_{\text{1-1-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{3^-{}_{\text{-11-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{3_{\text{-11-1}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{3^-{}_{\text{-1-11}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{3_{\text{-1-11}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{3}_{111}\right\} & \left\{\bar{3}^-{}_{111}\right\} & \left\{\bar{3}^-{}_{\text{1-1-1}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{\bar{3}_{\text{1-1-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{3}^-{}_{\text{-11-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{3}_{\text{-11-1}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{3}^-{}_{\text{-1-11}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{3}_{\text{-1-11}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} \\ \text{A}_1 & \text{A} & 2 & 0 & 0 & 0 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -2 & 0 & 0 & 0 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{A}_2 & \text{A} & 2 & 0 & 0 & 0 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & 2 & 0 & 0 & 0 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) \\ \text{A}_3 & \text{A} & 2 & 0 & 0 & 0 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -2 & 0 & 0 & 0 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{A}_4 & \text{A} & 2 & 0 & 0 & 0 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & 2 & 0 & 0 & 0 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) \\ \text{A}_5 & \text{C} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & -2 & 0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 \\ \text{A}_6 & \text{C} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \end{array} \right)\)
B \(\left(0,\frac{1}{2},0\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ \text{B}_1 & \text{A} & 2 & 0 & 0 & 0 & 0 & 0 & -2\mathrm{i}& 0 \\ \text{B}_2 & \text{A} & 2 & 0 & 0 & 0 & 0 & 0 & 2\mathrm{i}& 0 \\ \end{array} \right)\)
C \(\left(\frac{1}{2},\frac{1}{2},0\right)\) \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ \text{C}_1 & \text{A} & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 2\mathrm{i}\\ \text{C}_2 & \text{A} & 2 & 0 & 0 & 0 & 0 & 0 & 0 & -2\mathrm{i}\\ \end{array} \right)\)
D \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{2_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{3_{\text{1-1-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{3^-{}_{\text{-11-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{3_{\text{-11-1}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{3^-{}_{\text{-1-11}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{3_{\text{-1-11}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{3}_{111}\right\} & \left\{\bar{3}^-{}_{111}\right\} & \left\{\bar{3}^-{}_{\text{1-1-1}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{\bar{3}_{\text{1-1-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{3}^-{}_{\text{-11-1}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{3}_{\text{-11-1}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{3}^-{}_{\text{-1-11}},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{3}_{\text{-1-11}},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} \\ \text{D}_1 & \text{A} & 2 & 0 & 0 & 0 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -2 & 0 & 0 & 0 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{D}_2 & \text{A} & 2 & 0 & 0 & 0 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & 2 & 0 & 0 & 0 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) \\ \text{D}_3 & \text{A} & 2 & 0 & 0 & 0 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -2 & 0 & 0 & 0 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{D}_4 & \text{A} & 2 & 0 & 0 & 0 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & 2 & 0 & 0 & 0 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) \\ \text{D}_5 & \text{C} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & -2 & 0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 \\ \text{D}_6 & \text{C} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\ \end{array} \right)\)
\(D^1\) EAZ & character of irrep
\(a\) \(\left(\frac{1}{2},\frac{t}{2},\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} \\ a_1 & \text{A} & 1 & -\mathrm{i} e^{-\mathrm{i} \pi t} \\ a_2 & \text{A} & 1 &\mathrm{i}e^{-\mathrm{i} \pi t} \\ \end{array} \right)\)
\(b\) \(\left(\frac{1-t}{2},\frac{1-t}{2},\frac{1-t}{2}\right)\) \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} \\ b_1 & \text{D} & 1 & -1 & 1 \\ b_2 & \text{A} & 1 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ b_3 & \text{A} & 1 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \end{array} \right)\)
\(c\) \(\left(\frac{t}{2},0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ c_1 & \text{C} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(d\) \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} \\ d_1 & \text{C} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(e\) \(\left(\frac{1}{2},\frac{t}{2},0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ e_1 & \text{A} & 1 &\mathrm{i}& -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ e_2 & \text{A} & 1 &\mathrm{i}&\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ e_3 & \text{A} & 1 & -\mathrm{i} & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ e_4 & \text{A} & 1 & -\mathrm{i} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(f\) \(\left(\frac{1-t}{2},\frac{1}{2},0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,\frac{1}{2}\right\}\right\} & \left\{m_{001},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ f_1 & \text{A} & 1 &\mathrm{i}& -e^{\frac{i \pi t}{2}} & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ f_2 & \text{A} & 1 &\mathrm{i}& e^{\frac{i \pi t}{2}} &\mathrm{i}e^{\frac{i \pi t}{2}} \\ f_3 & \text{A} & 1 & -\mathrm{i} & -e^{\frac{i \pi t}{2}} &\mathrm{i}e^{\frac{i \pi t}{2}} \\ f_4 & \text{A} & 1 & -\mathrm{i} & e^{\frac{i \pi t}{2}} & -\mathrm{i} e^{\frac{i \pi t}{2}} \\ \end{array} \right)\)