| 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: | $C_6$ |
| Order: | $6$ |
| Abelian: | yes |
| Generators: | $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1/2 & \sqrt{3}/2 & 0 & 0 & 0 \\0 & -\sqrt{3}/2 & 1/2 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1/2 & \sqrt{3}/2 \\0 & 0 & 0 & 0 & -\sqrt{3}/2 & 1/2 \\\end{bmatrix}$ |
| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$3$ |
$0$ |
$38$ |
$0$ |
$715$ |
$0$ |
$16506$ |
$0$ |
$427686$ |
$0$ |
$11871948$ |
| $a_2$ |
$1$ |
$2$ |
$11$ |
$83$ |
$769$ |
$8078$ |
$91677$ |
$1093704$ |
$13501353$ |
$170832860$ |
$2202270145$ |
$28809609491$ |
$381384356519$ |
| $a_3$ |
$1$ |
$0$ |
$15$ |
$0$ |
$1984$ |
$0$ |
$434622$ |
$0$ |
$114737224$ |
$0$ |
$33307210695$ |
$0$ |
$10244879536012$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$3$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=4\right)\colon$ |
$11$ |
$6$ |
$19$ |
$38$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=6\right)\colon$ |
$15$ |
$83$ |
$47$ |
$162$ |
$95$ |
$337$ |
$715$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=8\right)\colon$ |
$123$ |
$769$ |
$438$ |
$254$ |
$1608$ |
$925$ |
$3458$ |
$1984$ |
$7523$ |
$16506$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=10\right)\colon$ |
$1221$ |
$8078$ |
$700$ |
$4579$ |
$2612$ |
$17543$ |
$9953$ |
$5666$ |
$38607$ |
$21850$ |
$85597$ |
$48314$ |
$190876$ |
$427686$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=12\right)\colon$ |
$1984$ |
$13273$ |
$91677$ |
$7526$ |
$51592$ |
$29118$ |
$203559$ |
$16472$ |
$114399$ |
$64418$ |
$455226$ |
$255284$ |
$143420$ |
$1023081$ |
| $$ |
$572534$ |
$2308602$ |
$1289400$ |
$5227374$ |
$11871948$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&0&1&0&2&3&0&1&0&3&0&0&6\\0&3&0&3&0&10&0&0&12&0&6&0&16&26&0\\1&0&8&0&7&0&17&22&0&12&0&32&0&0&70\\0&3&0&6&0&16&0&0&23&0&10&0&32&50&0\\1&0&7&0&11&0&22&23&0&19&0&45&0&0&92\\0&10&0&16&0&60&0&0&86&0&38&0&124&190&0\\2&0&17&0&22&0&60&67&0&52&0&120&0&0&268\\3&0&22&0&23&0&67&86&0&60&0&138&0&0&322\\0&12&0&23&0&86&0&0&138&0&58&0&200&311&0\\1&0&12&0&19&0&52&60&0&54&0&113&0&0&262\\0&6&0&10&0&38&0&0&58&0&32&0&92&136&0\\3&0&32&0&45&0&120&138&0&113&0&265&0&0&598\\0&16&0&32&0&124&0&0&200&0&92&0&312&468&0\\0&26&0&50&0&190&0&0&311&0&136&0&468&727&0\\6&0&70&0&92&0&268&322&0&262&0&598&0&0&1416\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&3&8&6&11&60&60&86&138&54&32&265&312&727&1416&677&705&1620&1328&359\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ | $a_2=3$ |
|---|
| $-$ | $1$ | $1/3$ | $0$ | $1/3$ | $0$ | $0$ | $0$ |
|---|
| $a_1=0$ | $1/3$ | $1/3$ | $0$ | $1/3$ | $0$ | $0$ | $0$ |
|---|
| $a_3=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
| $a_1=a_3=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
