MSG 40.203 \(A_2\)

\(D^0\) EAZ & character of irrep
A \(\left(0,0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{A}_1 & \text{D} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
B \(\left(0,1,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{B}_1 & \text{D} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
C \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{C}_1 & \text{D} & 1 & -\mathrm{i} \\ \text{C}_2 & \text{D} & 1 &\mathrm{i}\\ \end{array} \right)\)
D \(\left(\frac{1}{2},0,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{D}_1 & \text{A} & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ \text{D}_2 & \text{A} & 1 & -\mathrm{i} & -\mathrm{i} & 1 \\ \text{D}_3 & \text{A} & 1 &\mathrm{i}&\mathrm{i}& 1 \\ \text{D}_4 & \text{A} & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ \end{array} \right)\)
E \(\left(\frac{1}{2},1,0\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{E}_1 & \text{A} & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ \text{E}_2 & \text{A} & 1 & -\mathrm{i} & -\mathrm{i} & 1 \\ \text{E}_3 & \text{A} & 1 &\mathrm{i}&\mathrm{i}& 1 \\ \text{E}_4 & \text{A} & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ \end{array} \right)\)
F \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} \\ \text{F}_1 & \text{D} & 1 &\mathrm{i}\\ \text{F}_2 & \text{D} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(D^1\) EAZ & character of irrep
\(a\) \(\left(0,t,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} \\ a_1 & \text{A} & 1 & -\mathrm{i} \\ a_2 & \text{A} & 1 &\mathrm{i}\\ \end{array} \right)\)
\(b\) \(\left(0,0,t\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ b_1 & \text{A} & 2 & 0 & 0 & 0 \\ \end{array} \right)\)
\(c\) \(\left(0,\frac{t}{2},1-\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} \\ c_1 & \text{A} & 1 & -\mathrm{i} \\ c_2 & \text{A} & 1 &\mathrm{i}\\ \end{array} \right)\)
\(d\) \(\left(\frac{1}{2},t,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} \\ d_1 & \text{C} & 1 &\mathrm{i}\\ d_2 & \text{C} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(e\) \(\left(\frac{1}{2},0,t\right)\) \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ e_1 & \text{A} & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ e_2 & \text{A} & 1 & -\mathrm{i} & -\mathrm{i} & 1 \\ e_3 & \text{A} & 1 &\mathrm{i}&\mathrm{i}& 1 \\ e_4 & \text{A} & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ \end{array} \right)\)
\(f\) \(\left(\frac{1}{2},\frac{t}{2},1-\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100},\left\{\frac{1}{2},0,0\right\}\right\} \\ f_1 & \text{A} & 1 &\mathrm{i}\\ f_2 & \text{A} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(g\) \(\left(\frac{t}{2},0,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ g_1 & \text{A} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_2 & \text{A} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(h\) \(\left(\frac{t}{2},1,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{\frac{1}{2},0,0\right\}\right\} \\ h_1 & \text{A} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ h_2 & \text{A} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(i\) \(\left(\frac{t}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ i_1 & \text{D} & 1 \\ \end{array} \right)\)