MSG 7.29 \(\text{A''}\)

\(D^0\) EAZ & character of irrep
A \(\left(0,0,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{A}_1 & \text{AI} & 1 & -1 \\ \text{A}_2 & \text{AI} & 1 & 1 \\ \end{array} \right)\)
B \(\left(\frac{1}{2},0,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{B}_1 & \text{AI} & 1 & -1 \\ \text{B}_2 & \text{AI} & 1 & 1 \\ \end{array} \right)\)
C \(\left(\frac{1}{2},\frac{1}{2},0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{C}_1 & \text{AIII} & 1 & -1 \\ \text{C}_2 & \text{AIII} & 1 & 1 \\ \end{array} \right)\)
D \(\left(0,\frac{1}{2},0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{D}_1 & \text{AIII} & 1 & -1 \\ \text{D}_2 & \text{AIII} & 1 & 1 \\ \end{array} \right)\)
E \(\left(0,0,\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{E}_1 & \text{D} & 1 &\mathrm{i}\\ \text{E}_2 & \text{D} & 1 & -\mathrm{i} \\ \end{array} \right)\)
F \(\left(\frac{1}{2},0,\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{F}_1 & \text{D} & 1 &\mathrm{i}\\ \text{F}_2 & \text{D} & 1 & -\mathrm{i} \\ \end{array} \right)\)
G \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{G}_1 & \text{DIII} & 1 &\mathrm{i}\\ \text{G}_2 & \text{DIII} & 1 & -\mathrm{i} \\ \end{array} \right)\)
H \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{H}_1 & \text{DIII} & 1 &\mathrm{i}\\ \text{H}_2 & \text{DIII} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(D^1\) EAZ & character of irrep
\(a\) \(\left(\frac{t}{2},0,0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ a_1 & \text{A} & 1 & -1 \\ a_2 & \text{A} & 1 & 1 \\ \end{array} \right)\)
\(b\) \(\left(\frac{1}{2},\frac{t}{2},0\right)\) \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ b_1 & \text{CI} & 1 \\ \end{array} \right)\)
\(c\) \(\left(\frac{1-t}{2},\frac{1}{2},0\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ c_1 & \text{AIII} & 1 & -1 \\ c_2 & \text{AIII} & 1 & 1 \\ \end{array} \right)\)
\(d\) \(\left(\frac{t}{2},0,\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ d_1 & \text{A} & 1 &\mathrm{i}\\ d_2 & \text{A} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(e\) \(\left(\frac{1}{2},\frac{t}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ e_1 & \text{DIII} & 1 \\ \end{array} \right)\)
\(f\) \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ f_1 & \text{AIII} & 1 &\mathrm{i}\\ f_2 & \text{AIII} & 1 & -\mathrm{i} \\ \end{array} \right)\)
\(g\) \(\left(0,\frac{t}{2},0\right)\) \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ g_1 & \text{CI} & 1 \\ \end{array} \right)\)
\(h\) \(\left(0,\frac{t}{2},\frac{1}{2}\right)\) \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ h_1 & \text{DIII} & 1 \\ \end{array} \right)\)
\(i\) \(\left(\frac{1}{2},0,\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ i_1 & \text{A} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ i_2 & \text{A} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)
\(j\) \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ j_1 & \text{AIII} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ j_2 & \text{AIII} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\)