| Name: | $\mathrm{SU}(2)_3$ |
| $\mathbb{R}$-dimension: | $3$ |
| Description: | $\left\{\begin{bmatrix}\alpha I_3&\beta I_3\\ \gamma I_3& \delta I_3\end{bmatrix}: \begin{bmatrix}\alpha&\beta\\\gamma&\delta\end{bmatrix}\in\mathrm{SU}(2)\right\}$ |
Symplectic form: | $\begin{bmatrix} 0 & I_3\\ -I_3 & 0\end{bmatrix}$ |
| Hodge circle: | $u\mapsto \mathrm{diag}(u,u, u, \bar u, \bar u, \bar u)$ |
| Name: | $D_6$ |
| Order: | $12$ |
| Abelian: | no |
| Generators: | $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1/2 & \sqrt{3}/2 & 0 & 0 & 0 \\0 & -\sqrt{3}/2 & 1/2 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1/2 & \sqrt{3}/2 \\0 & 0 & 0 & 0 & -\sqrt{3}/2 & 1/2 \\\end{bmatrix}, \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0& 0 & 0 & 0 & -1 \\\end{bmatrix}$ |
| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$20$ |
$0$ |
$360$ |
$0$ |
$8260$ |
$0$ |
$213864$ |
$0$ |
$5936040$ |
| $a_2$ |
$1$ |
$2$ |
$8$ |
$48$ |
$402$ |
$4087$ |
$45972$ |
$547227$ |
$6751738$ |
$85419453$ |
$1101143724$ |
$14404829606$ |
$190692249942$ |
| $a_3$ |
$1$ |
$0$ |
$8$ |
$0$ |
$994$ |
$0$ |
$217328$ |
$0$ |
$57368794$ |
$0$ |
$16653607482$ |
$0$ |
$5122439794428$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$2$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=4\right)\colon$ |
$8$ |
$3$ |
$10$ |
$20$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=6\right)\colon$ |
$8$ |
$48$ |
$24$ |
$82$ |
$47$ |
$169$ |
$360$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=8\right)\colon$ |
$62$ |
$402$ |
$220$ |
$128$ |
$806$ |
$463$ |
$1730$ |
$990$ |
$3762$ |
$8260$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=10\right)\colon$ |
$612$ |
$4087$ |
$349$ |
$2292$ |
$1306$ |
$8776$ |
$4977$ |
$2836$ |
$19305$ |
$10926$ |
$42800$ |
$24150$ |
$95438$ |
$213864$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=12\right)\colon$ |
$994$ |
$6640$ |
$45972$ |
$3764$ |
$25802$ |
$14560$ |
$101790$ |
$8232$ |
$57201$ |
$32208$ |
$227616$ |
$127642$ |
$71720$ |
$511542$ |
| $$ |
$286270$ |
$1154304$ |
$644676$ |
$2613684$ |
$5936040$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&0&0&0&0&3&0&0&0&1&0&0&3\\0&2&0&1&0&5&0&0&6&0&3&0&7&14&0\\1&0&5&0&2&0&8&13&0&4&0&15&0&0&35\\0&1&0&4&0&8&0&0&11&0&4&0&18&24&0\\0&0&2&0&8&0&11&9&0&13&0&24&0&0&46\\0&5&0&8&0&30&0&0&43&0&19&0&62&95&0\\0&0&8&0&11&0&33&30&0&25&0&61&0&0&134\\3&0&13&0&9&0&30&50&0&28&0&66&0&0&161\\0&6&0&11&0&43&0&0&70&0&30&0&98&156&0\\0&0&4&0&13&0&25&28&0&33&0&58&0&0&131\\0&3&0&4&0&19&0&0&30&0&18&0&44&68&0\\1&0&15&0&24&0&61&66&0&58&0&134&0&0&299\\0&7&0&18&0&62&0&0&98&0&44&0&162&231&0\\0&14&0&24&0&95&0&0&156&0&68&0&231&366&0\\3&0&35&0&46&0&134&161&0&131&0&299&0&0&708\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&2&5&4&8&30&33&50&70&33&18&134&162&366&708&346&364&818&672&190\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ | $a_2=3$ |
|---|
| $-$ | $1$ | $1/6$ | $0$ | $1/6$ | $0$ | $0$ | $0$ |
|---|
| $a_1=0$ | $1/6$ | $1/6$ | $0$ | $1/6$ | $0$ | $0$ | $0$ |
|---|
| $a_3=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
| $a_1=a_3=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
