| Name: | $\mathrm{U}(1)\times\mathrm{SU}(2)$ |
| $\mathbb{R}$-dimension: | $4$ |
| Description: | $\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}:A\in \mathrm{U}(1)\subseteq\mathrm{SU}(2),\ B\in\mathrm{SU}(2)\right\}$ |
Symplectic form: | $\begin{bmatrix}J_2&0\\0&J_2\end{bmatrix}, J_2:=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ |
| Hodge circle: | $u\mapsto\mathrm{diag}(u,\bar u,\bar u,u)$ |
| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$11$ |
$0$ |
$90$ |
$0$ |
$889$ |
$0$ |
$9723$ |
$0$ |
$113322$ |
| $a_2$ |
$1$ |
$2$ |
$5$ |
$14$ |
$46$ |
$172$ |
$714$ |
$3180$ |
$14858$ |
$71732$ |
$354676$ |
$1786072$ |
$9127672$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$2$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$5$ |
$6$ |
$11$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$14$ |
$21$ |
$42$ |
$90$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$46$ |
$82$ |
$175$ |
$390$ |
$889$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$172$ |
$347$ |
$774$ |
$1774$ |
$4130$ |
$9723$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$714$ |
$1554$ |
$3572$ |
$8356$ |
$19768$ |
$47166$ |
$113322$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&0&0&1&0&0&0&1\\0&2&0&0&2&0&1&0&2&0\\1&0&2&1&0&2&0&2&0&2\\0&0&1&4&0&1&0&5&0&1\\0&2&0&0&5&0&4&0&6&0\\1&0&2&1&0&4&0&4&0&4\\0&1&0&0&4&0&6&0&5&0\\0&0&2&5&0&4&0&11&0&5\\0&2&0&0&6&0&5&0&11&0\\1&0&2&1&0&4&0&5&0&6\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&2&2&4&5&4&6&11&11&6\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
|---|
| $-$ | $1$ | $1/2$ | $0$ | $0$ | $0$ | $0$ | $1/2$ |
|---|
| $a_1=0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
