| 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: | $C_3$ |
| Order: | $3$ |
| Abelian: | yes |
| Generators: | $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & -1/2 & \sqrt{3}/2 & 0 & 0 & 0 \\0 &-\sqrt{3}/2 & -1/2 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & -1/2 & \sqrt{3}/2 \\0 & 0 & 0 & 0 & -\sqrt{3}/2 & -1/2 \\\end{bmatrix}$ |
| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$3$ |
$0$ |
$54$ |
$0$ |
$1215$ |
$0$ |
$30618$ |
$0$ |
$826686$ |
$0$ |
$23383404$ |
| $a_2$ |
$1$ |
$2$ |
$15$ |
$135$ |
$1377$ |
$15228$ |
$177633$ |
$2150550$ |
$26757945$ |
$340004142$ |
$4393068453$ |
$57538939923$ |
$762200653815$ |
| $a_3$ |
$1$ |
$0$ |
$23$ |
$0$ |
$3696$ |
$0$ |
$853742$ |
$0$ |
$228441640$ |
$0$ |
$66539338551$ |
$0$ |
$20483985509196$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$3$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=4\right)\colon$ |
$15$ |
$8$ |
$27$ |
$54$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=6\right)\colon$ |
$23$ |
$135$ |
$75$ |
$270$ |
$153$ |
$567$ |
$1215$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=8\right)\colon$ |
$211$ |
$1377$ |
$774$ |
$438$ |
$2916$ |
$1647$ |
$6318$ |
$3564$ |
$13851$ |
$30618$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=10\right)\colon$ |
$2241$ |
$15228$ |
$1266$ |
$8559$ |
$4824$ |
$33291$ |
$18711$ |
$10530$ |
$73629$ |
$41310$ |
$164025$ |
$91854$ |
$367416$ |
$826686$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=12\right)\colon$ |
$3696$ |
$25317$ |
$177633$ |
$14238$ |
$99468$ |
$55782$ |
$395847$ |
$31320$ |
$221373$ |
$123930$ |
$887922$ |
$495720$ |
$277020$ |
$2001105$ |
| $$ |
$1115370$ |
$4527090$ |
$2519424$ |
$10274526$ |
$23383404$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&0&1&0&4&5&0&3&0&5&0&0&12\\0&3&0&5&0&16&0&0&24&0&8&0&30&50&0\\1&0&12&0&11&0&31&40&0&26&0&58&0&0&140\\0&5&0&10&0&28&0&0&45&0&18&0&60&98&0\\1&0&11&0&15&0&40&45&0&37&0&81&0&0&184\\0&16&0&28&0&108&0&0&168&0&68&0&240&372&0\\4&0&31&0&40&0&112&131&0&104&0&230&0&0&532\\5&0&40&0&45&0&131&162&0&120&0&270&0&0&640\\0&24&0&45&0&168&0&0&270&0&114&0&396&615&0\\3&0&26&0&37&0&104&120&0&102&0&225&0&0&520\\0&8&0&18&0&68&0&0&114&0&56&0&180&268&0\\5&0&58&0&81&0&230&270&0&225&0&513&0&0&1192\\0&30&0&60&0&240&0&0&396&0&180&0&612&930&0\\0&50&0&98&0&372&0&0&615&0&268&0&930&1443&0\\12&0&140&0&184&0&532&640&0&520&0&1192&0&0&2820\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&3&12&10&15&108&112&162&270&102&56&513&612&1443&2820&1341&1401&3228&2640&707\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ | $a_2=3$ |
|---|
| $-$ | $1$ | $2/3$ | $0$ | $2/3$ | $0$ | $0$ | $0$ |
|---|
| $a_1=0$ | $2/3$ | $2/3$ | $0$ | $2/3$ | $0$ | $0$ | $0$ |
|---|
| $a_3=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
| $a_1=a_3=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
