Properties

 Label 1.6.J.2.1a Name $$J(E_2,E_1)$$ Weight $1$ Degree $6$ Real dimension $4$ Components $2$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{U}(1)\times\mathrm{SU}(2)_2$$ Component group $$C_2$$

Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $4$ Components: $2$ Contained in: $\mathrm{USp}(6)$ Rational: yes

Identity component

 Name: $\mathrm{U}(1)\times\mathrm{SU}(2)_2$ $\mathbb{R}$-dimension: $4$ Description: $\left\{\begin{bmatrix}A&0&0\\0&B&0\\0&0&\overline{B}\end{bmatrix}: A\in\mathrm{U}(1)\subseteq\mathrm{SU}(2),B\in\mathrm{SU}(2)\right\}$ Symplectic form: $\begin{bmatrix}J_2&0&0\\0&0&I_2\\0&-I_2&0\end{bmatrix},\ J_2:=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ Hodge circle: $\mathrm{diag}(u,\bar u, u,\bar u,\bar u,u)$

Component group

 Name: $C_2$ Order: $2$ Abelian: yes Generators: $\begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & i & 0 & 0 & 0 \\0 & 0 & 0 & i & 0 & 0 \\0 & 0 & 0 & 0 & -i & 0 \\0 & 0 & 0 & 0 & 0 & -i \\\end{bmatrix}$

Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $3$ $0$ $43$ $0$ $830$ $0$ $18627$ $0$ $458010$ $0$ $11976030$
$a_2$ $1$ $2$ $13$ $99$ $907$ $9188$ $99515$ $1129418$ $13270603$ $160175358$ $1975265743$ $24790641351$ $315730866109$
$a_3$ $1$ $0$ $18$ $0$ $2338$ $0$ $456520$ $0$ $107761906$ $0$ $28401505224$ $0$ $8045063991624$